A295818 - OEIS

%I #17 Nov 28 2017 18:01:08

%S 76333,80077,106243,115603,155333,175963,224683,279353,281207,299653,

%T 309157,312253,314267,318523,361093,413053,428083,526997,533893,

%U 573829,580093,605533,625237,637243,655987,661993,706633,708403,716747,723803,737293,740227,741347,741373,766967,775757,776267,776317

%N Primes p such that p+d is composite for all divisors d of p^2-1.

%C Primes n such that A295798(A000720(n)) = 0.

%C Primes n such that no semiprime with least prime factor n is in A143958.

%H Charles R Greathouse IV, <a href="/A295818/b295818.txt">Table of n, a(n) for n = 1..10000</a> (first 2000 from Robert Israel)

%p filter:= p -> isprime(p) and andmap(t -> not isprime(p+t), numtheory:-divisors(p^2-1)):

%p select(filter, [seq(i,i=3..10^6,2)]);

%o (PARI) is(n) = if(isprime(n), fordiv(n^2-1, d, if(isprime(n+d), return(0))); 1, 0) \\ _Iain Fox_, Nov 27 2017

%o (PARI) is(n)=my(o=valuation(n+1,2), f1=factor((n-1)<<o), f2=factor((n+1)>>o, f), f=Mat(vecsort(Vec(concat(f1~,f2~)),1))~); fordiv(f, d, if(isprime(n+d), return(0))); isprime(n) \\ _Charles R Greathouse IV_, Nov 28 2017

%Y Cf. A000720, A143958, A295798.

%K nonn

%O 1,1

%A _Robert Israel_, Nov 27 2017