A352926 Primes p such that there exist primes q, r (r != 2) such that p-1 = 2^q*r.

13, 29, 41, 53, 89, 97, 137, 149, 173, 233, 269, 293, 317, 353, 389, 509, 557, 569, 641, 653, 773, 797, 809, 857, 929, 1049, 1097, 1109, 1193, 1229, 1409, 1433, 1493, 1637, 1697, 1733, 1889, 1913, 1949, 1997, 2153, 2273, 2309, 2477, 2657, 2693, 2777, 2837

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Roberto Conti and Pierluigi Contucci, A Natural Avenue, arXiv:2204.08982 [math.NT], 2022.

Maple

f:= p-> (q-> andmap(isprime, [q, (p-1)/2^q]))(padic[ordp](p-1, 2)):
select(f, [ithprime(i)$i=1..500])[];  # Alois P. Heinz, May 01 2022

Mathematica

Select[Prime[Range[400]], PrimeQ[(q = IntegerExponent[# - 1, 2])] && PrimeQ[(# - 1)/2^q] &] (* Amiram Eldar, May 01 2022 *)

Prog

(Python)
from sympy import isprime, nextprime
from itertools import islice
def valuation(n, p):
    v = 0
    while n%p == 0: n //= p; v += 1
    return v, n
def agen(): # generator of terms
    p = 2
    while True:
        q, r = valuation(p-1, 2)
        if isprime(q) and isprime(r): yield p
        p = nextprime(p)
print(list(islice(agen(), 49))) # Michael S. Branicky, May 01 2022

Crossrefs

Cf. A005383, A352925.

Sequence in context: A240950 A141293 A339956 * A339989 A120827 A369863

Adjacent sequences: A352923 A352924 A352925 * A352927 A352928 A352929

Keyword

nonn

Author

N. J. A. Sloane, May 01 2022

Status

approved