cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A350705 Composite numbers that have no Sophie Germain prime and no "safe prime" factors.

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%I A350705 #25 Mar 17 2022 13:51:35
%S A350705 169,221,247,289,323,361,403,481,527,559,589,629,703,731,793,817,871,
%T A350705 923,949,961,1027,1037,1139,1147,1159,1207,1241,1261,1273,1313,1333,
%U A350705 1339,1343,1349,1369,1387,1417,1501,1591,1649,1651,1717,1751,1781,1807,1843,1849,1853
%N A350705 Composite numbers that have no Sophie Germain prime and no "safe prime" factors.
%C A350705 Prime factors of the terms have to be in A059500.
%H A350705 Karl-Heinz Hofmann, <a href="/A350705/b350705.txt">Table of n, a(n) for n = 1..10000</a>
%e A350705 a(2) = 221 = 13 * 17 and {13, 17} are neither in A005384 nor in A005385, but they are in A059500.
%t A350705 Select[Range[2000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], ! PrimeQ[2*#1 + 1] && ! PrimeQ[(#1 - 1)/2] &] &] (* _Amiram Eldar_, Feb 15 2022 *)
%o A350705 (Python)
%o A350705 from sympy import primefactors, isprime
%o A350705 print([n for n in range(2,1854) if not isprime(n) and all(not isprime(p*2+1) and not isprime((p-1)//2) for p in primefactors(n))])
%o A350705 (PARI) isok(m) = if ((m>1) && !isprime(m), my(f=factor(m)[,1]); !#select(x->isprime(2*x+1), f) && !#select(x->isprime((x-1)/2), f)); \\ _Michel Marcus_, Feb 14 2022
%Y A350705 Subsequence of A350704 and A350706.
%Y A350705 Cf. A005384, A005385, A053176, A059500.
%K A350705 nonn
%O A350705 1,1
%A A350705 _Karl-Heinz Hofmann_, Feb 14 2022