A263941 -id:A263941 - cp's OEIS frontend

A339531 Numbers b > 1 such that the smallest two primes, i.e., 2 and 3 are base-b Wieferich primes.

17, 37, 53, 73, 89, 109, 125, 145, 161, 181, 197, 217, 233, 253, 269, 289, 305, 325, 341, 361, 377, 397, 413, 433, 449, 469, 485, 505, 521, 541, 557, 577, 593, 613, 629, 649, 665, 685, 701, 721, 737, 757, 773, 793, 809, 829, 845, 865, 881, 901, 917, 937, 953

Offset: 1

Felix Fröhlich, Dec 08 2020

nonn

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A256236, A263941. Row 1 of A319059.

Cf. smallest k primes are base-b Wieferich primes: A339532 (k=3), A339533 (k=4), A339534 (k=5), A339535 (k=6), A339536 (k=7), A339537 (k=8).

Select[Range[2, 10^3], Function[b, AllTrue[{2, 3}, PowerMod[b, (# - 1), #^2] == 1 &]]] (* Michael De Vlieger, Dec 10 2020 *)

is(n) = forprime(p=1, 3, if(Mod(n, p^2)^(p-1)!=1, return(0))); 1

a(n) = 4*A263941(n) + 1 for n>=2, a(n) = 4*floor((9*n)/2) + 1 for all n. - Hugo Pfoertner, Dec 08 2020
From Chai Wah Wu, Aug 18 2025: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.
G.f.: x*(-x^2 + 20*x + 17)/((x - 1)^2*(x + 1)). (End)

A258589 Minimal most likely sum for a roll of n 12-sided dice.

Original entry on oeis.org

1, 13, 19, 26, 32, 39, 45, 52, 58, 65, 71, 78, 84, 91, 97, 104, 110, 117, 123, 130, 136, 143, 149, 156, 162, 169, 175, 182, 188, 195, 201, 208, 214, 221, 227, 234, 240, 247, 253, 260, 266, 273, 279, 286, 292, 299, 305, 312, 318, 325, 331, 338, 344, 351, 357

Offset: 1

Gianmarco Giordano, Nov 06 2015

			For n=1, there are twelve equally likely outcomes, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and the smallest of these is 1, so a(1)=1.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A030123, A256680, A263941, A258588.

Join[{1}, Table[(26 n + (-1)^n - 1)/4, {n, 2, 50}]]

a(n)=if(n<2, 1, 13*n\2);
vector(50, n, a(n))

a(n) = if(n<2,n, (26*n + (-1)^n - 1)/4);
vector(50, n, a(n))

Vec(-x*(5*x^3-5*x^2-12*x-1)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Nov 06 2015

a(n) = floor(13*n/2) = (26*n + (-1)^n - 1)/4 with n>1, a(1)=1.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>4.
G.f.: -x*(5*x^3-5*x^2-12*x-1) / ((x-1)^2*(x+1)). - Colin Barker, Nov 06 2015

A258588 Minimal most likely sum for a roll of n 10-sided dice.

Original entry on oeis.org

1, 11, 16, 22, 27, 33, 38, 44, 49, 55, 60, 66, 71, 77, 82, 88, 93, 99, 104, 110, 115, 121, 126, 132, 137, 143, 148, 154, 159, 165, 170, 176, 181, 187, 192, 198, 203, 209, 214, 220, 225, 231, 236, 242, 247, 253, 258, 264, 269, 275

Offset: 1

Gianmarco Giordano, Nov 06 2015

			For n=1, there are ten equally likely outcomes, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and the smallest of these is 1, so a(1)=1.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A030123, A256680, A263941.

Join[{1}, Table[(22 n + (-1)^n - 1)/4, {n, 2, 50}]]

a(n)=if(n<2, 1,11*n\2);
vector(50, n, a(n))

G.f.: x*(1 + 10*x + 4*x^2 - 4*x^3)/((1 - x)^2*(1 + x)).
a(n) = floor(11*n/2) = (22*n + (-1)^n - 1)/4 with n>1, a(1)=1.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>4.

cp's OEIS Frontend

A339531 Numbers b > 1 such that the smallest two primes, i.e., 2 and 3 are base-b Wieferich primes.

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A258589 Minimal most likely sum for a roll of n 12-sided dice.

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A258588 Minimal most likely sum for a roll of n 10-sided dice.

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Mathematica

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Formula