A295818 Primes p such that p+d is composite for all divisors d of p^2-1.

76333, 80077, 106243, 115603, 155333, 175963, 224683, 279353, 281207, 299653, 309157, 312253, 314267, 318523, 361093, 413053, 428083, 526997, 533893, 573829, 580093, 605533, 625237, 637243, 655987, 661993, 706633, 708403, 716747, 723803, 737293, 740227, 741347, 741373, 766967, 775757, 776267, 776317

Offset

1,1

Comments

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

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 2000 from Robert Israel)

Maple

filter:= p -> isprime(p) and andmap(t -> not isprime(p+t), numtheory:-divisors(p^2-1)):
select(filter, [seq(i, i=3..10^6, 2)]);

Prog

(PARI) is(n) = if(isprime(n), fordiv(n^2-1, d, if(isprime(n+d), return(0))); 1, 0) \\ Iain Fox, Nov 27 2017
(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

Crossrefs

Cf. A000720, A143958, A295798.

Sequence in context: A049026 A187424 A186216 * A183744 A236709 A104327

Adjacent sequences: A295815 A295816 A295817 * A295819 A295820 A295821

Keyword

nonn

Author

Robert Israel, Nov 27 2017

Status

approved