A072063 Smallest prime of form prime(n)+k*n, k>0.

3, 5, 11, 11, 31, 19, 31, 43, 41, 59, 53, 61, 67, 71, 107, 101, 127, 79, 181, 131, 157, 101, 313, 113, 197, 127, 157, 163, 167, 173, 251, 163, 269, 173, 359, 223, 379, 239, 401, 293, 1163, 223, 277, 281, 467, 337, 587, 271, 521, 379, 641, 499

Offset

1,1

Comments

According to Dirichlet's theorem primes of form prime(n)+k*n exist for all n, as gcd(n, prime(n))=1.

Nontrivial least prime == prime(n) (mod n).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

n=3, prime(3)=5: 5+1*3=8 is not prime, but 5+2*3=11, therefore a(3)=11 and A072064(3)=2.

Maple

f:= proc(n) local p, k, k0;
  p:= ithprime(n);
  if n::odd then k0:= 2 else k0:= 1 fi;
  for k from k0 by k0 do
    if isprime(p+k*n) then return p+k*n fi
  od:
end proc:
f(1):= 3:
map(f, [$1..100]); # Robert Israel, Nov 27 2023

Mathematica

sp[n_]:=Module[{p=Prime[n], k=1}, While[!PrimeQ[p+k*n], k++]; p+k*n]; Array[ sp, 60] (* Harvey P. Dale, Apr 19 2019 *)

Prog

(PARI) a072063(n) = {my (p=prime(n), j); for (k=1, oo, if(isprime(j=p+k*n), return(j)))}; \\ Hugo Pfoertner, Nov 27 2023

Crossrefs

Cf. A034694, A000040, A061068, A072064.

Cf. A090471, A090472, A090473.

Sequence in context: A273037 A006538 A066281 * A242269 A309426 A115398

Adjacent sequences: A072060 A072061 A072062 * A072064 A072065 A072066

Keyword

nonn

Author

Reinhard Zumkeller, Jun 12 2002

Status

approved