Propose OEIS sequences - Githubissues

Smallest starting value of exactly n-1 numbers with exactly n divisors, or 0 if no such number exists: (cf. A072507, A292580)

a(n) for n = 2 to 11: 5, 0, 33, 0, 10093613546512321, 0, 171893, 0, 0, 0

5 should be replaced by 2 if we use "at least n-1 numbers" instead of "exactly n-1 numbers"

a(12) <= 677667095479412562100444 (a(12) <= 247239052981730986799644 if we use "at least n-1 numbers" instead of "exactly n-1 numbers)

Smallest base b such that n is a unique period (related to unique prime) (cf. A085398):

a(n) for n = 1 to 100: 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 2, 22, 2, 2, 4, 6, 2, 2, 2, 2, 2, 14, 3, 61, 2, 10, 2, 14, 2, 15, 25, 11, 2, 5, 5, 2, 6, 30, 11, 24, 2, 7, 2, 5, 7, 19, 3, 2, 2, 3, 3, 2, 9, 46, 47, 2, 3, 3, 3, 11, 16, 59, 7, 2, 2, 22, 2, 21, 61, 41, 7, 2, 2, 8, 5, 2, 2, 11, 4, 2, 6, 44, 4, 12, 2, 63, 20

If n = 10*m+d with 0<=d<=9, a(n) = largest nonnegative integer k such that m^k does not contain the digit d (or -1 if there are infinitely many such k, -2 if no such k exists).
Triangle read by rows: a(m,n) = the gcd(m,n)-th number k such that sigma(k)/k = m/n (i.e. the abundancy of k is m/n, note that the abundancy is always >=1 and rational number), or 0 if no such k exists, for 1<=n<=m

All positive integers appear in this triangle exactly once (only 0 appears infinitely many times), however, computing this triangle is very hard, related topics: friendly number, multiply perfect number, hemiperfect number

This triangle begins with:

1 (1 is the first (and the only) number k such that sigma(k)/k = 1/1 = 1) 6, 0 (6 is the first number k such that sigma(k)/k = 2/1 = 2, and there is no second number k such that sigma(k)/k = 2/2 = 1, 1 is the only one such number) 120, 2, 0 (120 is the first number k such that sigma(k)/k = 3/1 = 3, 2 is the first number k such that sigma(k)/k = 3/2, and there is no third number k such that sigma(k)/k = 3/3 = 1, 1 is the only one such number) 30240, 28, 3, 0 (30240 is the first number k such that sigma(k)/k = 4/1 = 4, 28 is the second number k such that sigma(k)/k = 4/2 = 2, 3 is the first number k such that sigma(k)/k = 4/3, and there is no fourth number k such that sigma(k)/k = 4/4 = 1, 1 is the only one such number) 14182439040, 24, (unknown, there is no k <= 2^24 such that sigma(k)/k = 5/3), (unknown, there is no k <= 2^24 such that sigma(k)/k = 5/4), 0 154345556085770649600, 672 (the second k such that sigma(k)/k = 6/2 = 3), 496, 0 (2 is solitary number, thus there is no second number k such that sigma(k)/k = 3/2), 5, 0 141310897947438348259849402738485523264343544818565120000, 4320, 12, 4, (unknown), (unknown), 0 8268099687077761372899241948635962893501943883292455548843932421413884476391773708366277840568053624227289196057256213348352000000000, 32760, 84, 8128, 15, 0 (3 is solitary number, thus there is no second number k such that sigma(k)/k = 4/3), 7, 0 ... keywords: nonn, tabl, more, hard

Square array read by antidiagonals: A(m,n) is the number of cycles of the Kapakar maps of n-digit base m numbers.
Numbers k which is a totient but not a totient of squarefree numbers.
Number of steps in Conway's Game of Life for the free polyomino represented by A246521(n) to stabilize (cf. A246521, A152389, A335573), a(1) through a(22) are 0, 1, 1, 1, 0, 3, 0, 9, 2, 2, 4, 3, 2, 9, 3, 5, 4, 10, 1103, 3, 8, 6
Position of the start of the first occurrence of the string of digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11, 12, 13, 14, …) in Pi (or e or gamma or …), cf.
Irregular triangle listed the coefficients of The Lucas C, D polynomials (create two sequences, one of the C polynomials and the other of the D polynomials)
Numbers which when converted to bijective base 26 (A=1, B=2, ..., Z=26) make English words. (cf. A038842)
Smallest triangular number with prime signature the same as A025487(n), or 0 if no such number exists (cf. A081978, also create the sequence of tetrahedral number instead of triangular number, cf, A279082)
Relative class number h- of cyclotomic field Q(zeta_2n), cf. A061494, A035115, A061653, also create the sequence of the full class number h = h- * h+
Smallest base which have a Sierpinski/Riesel number with n-cover (i.e. modulus n), cf. A146563, A257647, A258154, a(prime(n)) = A146563(n) (the offset of A146563 should be 1 instead of 2), a(n) = 2 if and only if A257647(n/2) and A258154(n/2) are nonzero (only consider even n)

a(1) through a(14) are 3, 14, 74, 8, 339, 9, 2601, 8, 9, 25, 32400, 5, 212574, 51

the 6-cover of base 9 is (5, 7, 13, 73) the 8-cover of base 8 can be (3, 5, 17, 241) or (3, 13, 17, 241) the 9-cover of base 9 is (7, 13, 19, 37, 757) the 10-cover of base 25 is (11, 13, 41, 71, 521, 9161) the 12-cover of base 5 is (3, 7, 13, 31, 601) the 14-cover of base 51 is (13, 29, 43, 71, 421, 463,11411, 1572887)

Please fill the holes of "numbers n such that k10^n+1 is prime" and "numbers n such that k10^n-1 is prime" for k<100 (except the k divisible by 10, and the k which have no possible primes)

For k*10^n-1, I found https://oeis.org/A002957, https://oeis.org/A056703, https://oeis.org/A056712, https://oeis.org/A056716, https://oeis.org/A056721, https://oeis.org/A056725, https://oeis.org/A111391, https://oeis.org/A257036, https://oeis.org/A257037, https://oeis.org/A257038, https://oeis.org/A257039, https://oeis.org/A257040, https://oeis.org/A257041 in OEIS but did not found 12 ≤ k ≤ 89 in OEIS

archmageirvine / joeis

Propose OEIS sequences #7