A355161 Primes p such that p - prevprime(p) is not a power of 2.

29, 37, 53, 59, 67, 79, 89, 127, 137, 149, 157, 163, 173, 179, 191, 211, 223, 239, 251, 257, 263, 269, 277, 293, 307, 331, 337, 347, 359, 373, 379, 389, 419, 431, 439, 449, 479, 509, 521, 541, 547, 557, 563, 569, 577, 587, 593, 599, 607, 613

Offset: 1

Author

Reed Michael Upson, Jun 21 2022

Keywords

• nonn

Comments

A130796(n) is prevprime(p).

A031925 and A031931 are subsequences, as 6 and 12 are not powers of 2.

Crossrefs

Cf. A000079, A031925, A031931, A130796, A151800.

Programs

Mathematica

Select[Prime[Range[2, 120]], (d = # - NextPrime[#, -1]) != 2^IntegerExponent[d, 2] &] (* Amiram Eldar, Jun 22 2022 *)

PARI

isp2(n) = my(p); (n==1) || (isprimepower(n, &p) && (p==2)); \\ A000079
isok(p) = isprime(p) && !isp2(p-precprime(p-1)) \\ Michel Marcus, Jun 22 2022

Python

from itertools import islice, count
from sympy import prime, prevprime
def A355161_gen(): # generator of terms
    return filter(lambda n:((~(m:=n-prevprime(n))+1)&m)-m, (prime(n) for n in count(2)))
A355161_list = list(islice(A355161_gen(),30)) # Chai Wah Wu, Aug 23 2022

Formula

a(n) = A151800(A130796(n)).