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

1,1

Comments

A130796(n) is prevprime(p).

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

Links

Table of n, a(n) for n=1..50.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A234973 A134100 A060769 * A031925 A325058 A107134

Adjacent sequences: A355158 A355159 A355160 * A355162 A355163 A355164

Keyword

nonn

Author

Reed Michael Upson, Jun 21 2022

Status

approved