A181483 -id:A181483 - cp's OEIS frontend

A180303 a(n) = smallest number such that 3^n-2^a(n) is prime, or -1 if no such number exists.

0, 1, 2, 1, 1, 1, 3, 3, 1, 7, 4, 11, 6, 3, 4, 9, 9, 5, 6, 3, 2, 1, 7, 35, 12, 29, 10, 13, 6, 11, 2, 21, 8, 27, 11, -1, 1, 17, 10, -1, 1, 37, 8, 9, 16, 61, 23, 23, 17, 27, 4, 7, 2, 7, 7, 39, 58, 81, 30, 17, 60, 3, 8, 13, 18, -1, 20, 101, 4, 73, 27, 17, 2, 17, 19, 13, 41, 53, 44, 111, 34, 13

Offset: 1

Carl R. White, Aug 25 2010

sign

From Carl R. White, Oct 23 2010: (Start)
Entries where a(n) = 1 can be found in A014224.
Entries where a(n) = -1 can be found in A181484. (End)

			3^1-2^0 = 2, so a(1)=0; no other terms are zero.
3^11-2^1, 3^11-2^2, 3^11-2^3 are all nonprime, but 3^11-2^4 = 177131 which is prime so a(11) = 4.
a(36) is -1 (the placeholder value) because nonprimes are obtained when any power of two is subtracted from 3^36.

Cf. A013604.

Cf. A014224, A181483, A181484. - Carl R. White, Oct 23 2010

A181484 Numbers k such that no power of 2 can be subtracted from 3^k to make a prime.

Original entry on oeis.org

36, 40, 66, 124, 162, 170, 179, 182, 184, 198, 206, 212, 214, 230, 262, 288, 302, 356, 358, 368, 393, 402, 406, 448, 456, 468, 493, 546, 586, 666, 676, 683, 686, 690, 702, 718, 724, 738, 752, 760, 785, 844, 854, 862, 866, 870, 882, 884, 888, 904, 918, 980

Offset: 1

Carl R. White, Oct 23 2010

nonn

Zeros of A181483, -1s of A180303.

Odd terms: 179, 393, 493, 683, 785, 1083, 1161, 1181, 1545, ..., . - Robert G. Wilson v, Oct 25 2010

Cf. A013604, A014224, A180303, A181483.

fQ[n_] := Block[{k = 0, lmt = Floor@ Log[2, 3^n] +1, m = 3^n}, While[ k < lmt && !PrimeQ[m - 2^k], k++ ]; k == lmt]; Select[ Range@ 995, fQ] (* Robert G. Wilson v, Oct 25 2010 *)

a(30) onwards from Robert G. Wilson v, Oct 25 2010

Name clarified by J. Lowell, Aug 21 2020

cp's OEIS Frontend

A180303 a(n) = smallest number such that 3^n-2^a(n) is prime, or -1 if no such number exists.

Views

Author

Keywords

Comments

Examples

Crossrefs

A181484 Numbers k such that no power of 2 can be subtracted from 3^k to make a prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions