A343908 a(n) is the least prime == 4 (mod prime(n)).

2, 7, 19, 11, 37, 17, 89, 23, 73, 149, 97, 41, 127, 47, 239, 163, 181, 431, 71, 359, 223, 83, 419, 271, 101, 307, 107, 967, 113, 569, 131, 397, 1237, 421, 2239, 457, 1103, 167, 839, 523, 541, 547, 577, 197, 1777, 601, 1481, 227, 3863, 233, 3499, 2633, 727, 757, 1289, 1319, 811, 1901, 281, 1409

Offset: 1

Author

Zak Seidov, May 03 2021

Keywords

• nonn

Examples

			a(3) = 19 because 19 is the least prime == 4 (mod prime(3)).
a(4) = 11 because 11 is the least prime == 4 (mod prime(4)).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A023200 (primes p such that p+4 is also prime), A034694, A035095, A279756.

Programs

Maple

a:= proc(n) local q, p; p:= ithprime(n); q:= p;
      do if irem(q-4, p)=0 then break fi;
         q:= nextprime(q);
      od; q
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, May 03 2021

Mathematica

s = {}; p = 5; Do[q = p + 2; While[Mod[q, p] != 4, q = NextPrime[q]]; AppendTo[s, q]; p = NextPrime[p], {100}]; s

PARI

a(n) = my(p=prime(n)); forprime(q=2,, if (Mod(q, p) == 4, return(q))); \\ Michel Marcus, May 03 2021