A378839 a(n) is the least prime p such that p + 8*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.

2, 3, 151, 181, 13, 811, 23671, 92221, 45417481, 5078503, 4861, 20379346831, 12180447943, 31, 10347699089473

Offset: 1

Author

J.W.L. (Jan) Eerland, Dec 09 2024

Keywords

• nonn
• more

Comments

No further terms < 2.5*10^11. - Michael S. Branicky, Dec 16 2024

Crossrefs

Cf. A164926, A370387, A371024, A376675.

Programs

Maple

f:= proc(p) local k;
  for k from 1 while isprime(p+k*(k+1)*8) do od:
  k
end proc:
A:= Vector(12): count:= 0:
for i from 1 while count < 12 do
  v:= f(ithprime(i));
  if A[v] = 0 then count:= count+1; A[v]:= ithprime(i) fi
od:
convert(A,list);

Mathematica

Table[p=1;m=8;Monitor[Parallelize[While[True,If[And[MemberQ[PrimeQ[Table[p+m*k*(k+1),{k,0,n-1}]],False]==False,PrimeQ[p+m*n*(n+1)]==False],Break[]];p++];p],p],{n,1,10}]

PARI

isok(p, n) = for (k=0, n-1, if (! isprime(p + 8*k*(k+1)), return(0))); return (!isprime(p + 8*n*(n+1)));
a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p;

Perl

use ntheory qw(:all); sub a { my $n = $[0]; my $lo = 2; my $hi = 2*$lo; while (1) { my @terms = grep { !is_prime($ + 8*$n*($n+1)) } sieve_prime_cluster($lo, $hi, map { 8*$*($+1) } 1 .. $n-1); return $terms[0] if @terms; $lo = $hi+1; $hi = 2*$lo; } }; $| = 1; for my $n (1..100) { print a($n), ", " }; #

Extensions

a(12)-a(14) from Michael S. Branicky, Dec 15 2024

a(15) from Daniel Suteu, Dec 17 2024