A256072 - OEIS

%I #17 Oct 16 2024 08:16:42

%S 2,3,5,7,13,37,61,73,157,193,277,313,397,421,457,541,613,661,673,733,

%T 757,877,997,1093,1153,1201,1213,1237,1321,1381,1453,1621,1657,1753,

%U 1873,1933,1993,2017,2137,2341,2473,2557,2593,2797,2857,2917,3061,3217,3253,3313

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

%C Primes in A254636.

%F {2, 7} UNION A005383 = {7} UNION A079147. - _Chai Wah Wu_, Oct 15 2024

%o (Python)

%o import sympy

%o from sympy import isprime

%o TOP = 10000

%o a = [0]*TOP

%o for y in range(2, TOP//2):

%o   for x in range(y, TOP//2):

%o     k = x*y + x + y

%o     if k>=TOP: break

%o     a[k]+=1

%o print([n for n in range(TOP) if a[n]==0 and isprime(n)])

%o (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 Cf. A000040, A254636, A005383, A079147.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Mar 14 2015