A355849 a(n) is the least k > 1 such that k*n is the average of two consecutive primes.

4, 2, 2, 3, 3, 2, 3, 7, 2, 3, 9, 5, 2, 3, 2, 4, 2, 4, 4, 3, 2, 7, 3, 3, 2, 10, 3, 2, 12, 2, 3, 2, 3, 3, 3, 2, 3, 2, 5, 3, 5, 10, 2, 4, 4, 3, 6, 3, 9, 3, 2, 5, 12, 2, 3, 10, 4, 6, 4, 2, 10, 3, 5, 3, 3, 3, 2, 8, 2, 6, 6, 2, 10, 5, 2, 3, 2, 4, 14, 2, 4, 3, 9, 5, 2, 12, 4, 2, 4, 2, 12, 6, 2, 3, 6, 2

Offset: 1

Author

J. M. Bergot and Robert Israel, Jul 28 2022

Keywords

• nonn

Comments

a(n) is the least k > 1 such that k*n is in A024675.

Examples

			a(4) = 3 because 3*4 = 12 is the average of consecutive primes 11 and 13.
		

Links

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

Crossrefs

Cf. A024675.

Programs

Maple

M:= {seq((ithprime(i)+ithprime(i+1))/2, i=2..10^5)}:
f:= proc(p) local k;
  for k from 2 do if member(k*p,M) then return k fi od
end proc:
map(f, [$1..100]);

Mathematica

a[n_] := Module[{m = 2*n}, While[Plus @@ NextPrime[m, {-1, 1}] != 2*m, m += n]; m/n]; Array[a, 100] (* Amiram Eldar, Aug 05 2022 *)