A343418 Primes that occur in A343416.

11, 29, 41, 61, 73, 97, 131, 137, 139, 149, 151, 157, 167, 179, 191, 211, 227, 229, 233, 241, 251, 283, 293, 307, 313, 331, 347, 373, 383, 389, 397, 401, 449, 463, 521, 577, 607, 631, 641, 647, 653, 661, 673, 677, 701, 709, 719, 727, 757, 769, 811, 821, 823, 829, 857, 859, 877, 887, 907, 919, 929

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 14 2021

Keywords

• nonn

Comments

Terms are distinct and in numerical order, not the order they occur in A343416.

If p, 6*p-1 and 19*p+4 are prime, then 19*p+4 = A343416(6*p-1) is a term. Dickson's conjecture implies that there are infinitely many such terms.

Examples

			a(3) = 41 is a term because 41 = A343416(8) = A343416(10) and is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A343416.

Programs

Maple

spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
f:= proc(n) local a,b;
  a:= spf(n);
  b:= numtheory:-sigma(n);
  a+b+spf(b)+numtheory:-sigma(a)
end proc:
S:= select(t -> t < 1000 and isprime(t), map(f, {$1..1000})):
sort(convert(S,list));