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

1,1

Comments

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

Links

Table of n, a(n) for n=1..15.

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}]

Prog

(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), ", " }; #

Crossrefs

Cf. A164926, A370387, A371024, A376675.

Sequence in context: A124236 A371272 A115231 * A371231 A042369 A371273

Adjacent sequences: A378836 A378837 A378838 * A378840 A378841 A378842

Keyword

nonn,more

Author

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

Extensions

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

a(15) from Daniel Suteu, Dec 17 2024

Status

approved