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A256072 Primes that cannot be represented as x*y + x + y, where x >= y > 1.

%I A256072 #17 Oct 16 2024 08:16:42
%S A256072 2,3,5,7,13,37,61,73,157,193,277,313,397,421,457,541,613,661,673,733,
%T A256072 757,877,997,1093,1153,1201,1213,1237,1321,1381,1453,1621,1657,1753,
%U A256072 1873,1933,1993,2017,2137,2341,2473,2557,2593,2797,2857,2917,3061,3217,3253,3313
%N A256072 Primes that cannot be represented as x*y + x + y, where x >= y > 1.
%C A256072 Primes in A254636.
%F A256072 {2, 7} UNION A005383 = {7} UNION A079147. - _Chai Wah Wu_, Oct 15 2024
%o A256072 (Python)
%o A256072 import sympy
%o A256072 from sympy import isprime
%o A256072 TOP = 10000
%o A256072 a = [0]*TOP
%o A256072 for y in range(2, TOP//2):
%o A256072   for x in range(y, TOP//2):
%o A256072     k = x*y + x + y
%o A256072     if k>=TOP: break
%o A256072     a[k]+=1
%o A256072 print([n for n in range(TOP) if a[n]==0 and isprime(n)])
%o A256072 (PARI) v=[];for(m=2,500,for(k=m,500,if(isprime(P=k*m+k+m),v=concat(v,P))));v=vecsort(v,,8);forprime(p=1,2000,if(!vecsearch(v,p),print1(p,", "))) \\ _Derek Orr_, Mar 21 2015
%Y A256072 Cf. A000040, A254636, A005383, A079147.
%K A256072 nonn
%O A256072 1,1
%A A256072 _Alex Ratushnyak_, Mar 14 2015