A130796 -id:A130796 - cp's OEIS frontend

A258578 Primes p such that difference between p and next prime after p is multiple of 6.

23, 31, 47, 53, 61, 73, 83, 131, 151, 157, 167, 173, 199, 211, 233, 251, 257, 263, 271, 331, 353, 367, 373, 383, 433, 443, 467, 503, 509, 523, 541, 557, 563, 571, 587, 593, 601, 607, 619, 647, 653, 661, 677, 727, 733, 751, 797, 941, 947, 971, 977, 991, 997

Offset: 1

Zak Seidov, Jun 04 2015

nonn

A031924 is subsequence: first 12 terms are the same.

			a(1)=23 because next prime after 23 is 29=23+6,
a(13)=199 because next prime after 199 is 211=199+12,
a(30)=523 because next prime after 523 is 541=523+18,
a(90)=1669 because next term after 1669 is 1693=1669+24,
a(199)=4297 because next prime after 4297 is 4327=4297+30.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A031924, A124582, A130796.

Select[Partition[Prime[Range[200]],2,1],Mod[#[[2]]-#[[1]],6]==0&][[All,1]] (* Harvey P. Dale, Jun 20 2019 *)

lista(nn) = forprime(p=2, nn, if (!((nextprime(p+1) - p) % 6), print1(p, ", "));); \\ Michel Marcus, Jun 04 2015

v=List();p=2; forprime(q=3,1e4,if((q-p)%6==0,listput(v,p));p=q); v \\ Charles R Greathouse IV, Jun 04 2015

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

Original entry on oeis.org

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

Reed Michael Upson, Jun 21 2022

nonn

A130796(n) is prevprime(p).

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

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

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

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

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

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

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A258578 Primes p such that difference between p and next prime after p is multiple of 6.

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

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