A352925 Primes p such that there exist primes q, r (r != 2) such that p+1 = 2^q*r.

11, 19, 23, 43, 67, 103, 151, 163, 211, 223, 283, 331, 383, 487, 523, 547, 607, 631, 691, 787, 823, 907, 991, 1051, 1123, 1171, 1303, 1447, 1531, 1543, 1663, 1723, 1783, 1831, 1867, 1951, 2011, 2083, 2143, 2251, 2347, 2371, 2467, 2503, 2647, 2707, 2731, 2791

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, A352926.

Sequence in context: A352480 A031406 A280993 * A105908 A084654 A089172

Adjacent sequences: A352922 A352923 A352924 * A352926 A352927 A352928

Keyword

nonn

Author

N. J. A. Sloane, May 01 2022

Extensions

a(12) and beyond from Michael S. Branicky, May 01 2022

Status

approved