cp's OEIS Frontend

A382887 Numbers k such that (k*2^d + 1)*(d*2^k + 1) is semiprime for some divisor d of k.

%I A382887 #25 Apr 16 2025 05:42:04
%S A382887 1,2,8,12,30,51,63,141,201,209,534,4713,5795,6611,7050,18496,24105,
%T A382887 32292,32469,52782,59656,80190,90825
%N A382887 Numbers k such that (k*2^d + 1)*(d*2^k + 1) is semiprime for some divisor d of k.
%C A382887 a(24) > 10^5. - _Michael S. Branicky_, Apr 08 2025
%e A382887 12 is in this sequence because (12*2^3 + 1)*(3*2^12 + 1) = 97*12289 is semiprime for divisor 3 of 12.
%o A382887 (Magma) [n: n in [1..1000] | not #[d: d in Divisors(n) | IsPrime(d*2^n+1) and IsPrime(n*2^d+1)] eq 0];
%o A382887 (Python)
%o A382887 from itertools import count, islice
%o A382887 from sympy import isprime, divisors
%o A382887 def A382887_gen(): # generator of terms
%o A382887     yield from filter(lambda k:any(isprime((k<<d)+1) and isprime((d<<k)+1) for d in divisors(k,generator=True)),count(1))
%o A382887 A382887_list = list(islice(A382887_gen(),10)) # _Chai Wah Wu_, Apr 15 2025
%o A382887 (PARI) isok(k) = fordiv(k, d, if (ispseudoprime(k*2^d+1) && ispseudoprime(d*2^k+1), return(1))); \\ _Michel Marcus_, Apr 16 2025
%Y A382887 Supersequence of A005849.
%Y A382887 Cf. A001358, A002064, A382646.
%K A382887 nonn,more
%O A382887 1,2
%A A382887 _Juri-Stepan Gerasimov_, Apr 07 2025
%E A382887 a(10) inserted and a(15)-a(23) from _Michael S. Branicky_, Apr 08 2025