A378841 a(n) is the least prime p such that p + 9*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.
2, 11, 13, 5, 19, 173, 3163, 83, 21013, 878359, 3676219, 239, 43, 5201390418463, 86927887467919
Offset: 1
Programs
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Maple
f:= proc(p) local k; for k from 1 while isprime(p+k*(k+1)*9) 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);
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Mathematica
Table[p=1;m=9;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 + 9*k*(k+1)), return(0))); return (!isprime(p + 9*n*(n+1))); a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p;
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Perl
use ntheory qw(:all); sub a { my $n = $[0]; my $lo = 2; my $hi = 2*$lo; while (1) { my @terms = grep { !is_prime($ + 9*$n*($n+1)) } sieve_prime_cluster($lo, $hi, map { 9*$*($+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(14) from Daniel Suteu, Dec 17 2024
a(15) from Daniel Suteu, Dec 22 2024