A381970 Numbers k such that there are no primes of the form 2^(k-m)*3^m + 1 or 2^(k-m)*3^m - 1 for 0 <= m <= k.

46, 74, 102, 118, 130, 142, 162, 165, 166, 186, 200, 234, 242, 252, 258, 306, 318, 358, 370, 374, 414, 462, 478, 494, 506, 518, 522, 538, 540, 550, 578, 594, 618, 630, 654, 662, 666, 672, 690, 738, 750, 768, 778, 780, 790, 802, 810, 826, 834, 858, 886, 902, 912, 938, 942, 958, 982, 990, 1002

Offset: 1

Author

Robert Israel, Mar 11 2025

Keywords

• nonn

Comments

Numbers k such that A167506(k) = 0.

Mark Underwood observed that there are no primes < 3187 in this sequence.

The first two odd terms are 165 and 3615.

One reason why there are so many more even terms than odd terms is that if k is even, one of 2^(k-m)*3^m + 1 and 2^(k-m)*3^m - 1 is always divisible by 5, while if k is odd, neither is divisible by 5.

Links

• Robert Israel, Table of n, a(n) for n = 1..200
• Mark Underwood and Jens Kruse Andersen, 2^a*3^b one away from a prime, digest of 3 messages in primenumbers Yahoo group, Nov 19, 2009.

Crossrefs

Cf. A167506.

Programs

Maple

g:= proc(n,m) local t; t:= 2^(n-m)*3^m; isprime(t+1) or isprime(t-1) end proc:
filter:= proc(n) not ormap(m -> g(n,m), [$0..n]) end proc:
select(filter, [$1..1000]);