A352925 - OEIS

%I #15 May 01 2022 13:22:10

%S 11,19,23,43,67,103,151,163,211,223,283,331,383,487,523,547,607,631,

%T 691,787,823,907,991,1051,1123,1171,1303,1447,1531,1543,1663,1723,

%U 1783,1831,1867,1951,2011,2083,2143,2251,2347,2371,2467,2503,2647,2707,2731,2791

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

%H Michael S. Branicky, <a href="/A352925/b352925.txt">Table of n, a(n) for n = 1..10000</a>

%H Roberto Conti and Pierluigi Contucci, <a href="https://arxiv.org/abs/2204.08982">A Natural Avenue</a>, arXiv:2204.08982 [math.NT], 2022.

%p f:= p-> (q-> andmap(isprime, [q, (p+1)/2^q]))(padic[ordp](p+1, 2)):

%p select(f, [ithprime(i)$i=1..500])[];  # _Alois P. Heinz_, May 01 2022

%t Select[Prime[Range[400]], PrimeQ[(q = IntegerExponent[# + 1, 2])] && PrimeQ[(# + 1)/2^q] &] (* _Amiram Eldar_, May 01 2022 *)

%o (Python)

%o from sympy import isprime, nextprime

%o from itertools import islice

%o def valuation(n, p):

%o     v = 0

%o     while n%p == 0: n //= p; v += 1

%o     return v, n

%o def agen(): # generator of terms

%o     p = 2

%o     while True:

%o         q, r = valuation(p+1, 2)

%o         if isprime(q) and isprime(r): yield p

%o         p = nextprime(p)

%o print(list(islice(agen(), 49))) # _Michael S. Branicky_, May 01 2022

%Y Cf. A005383, A352926.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, May 01 2022

%E a(12) and beyond from _Michael S. Branicky_, May 01 2022