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

1,1

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A024675.

Sequence in context: A112349 A231821 A062072 * A140395 A061505 A255708

Adjacent sequences: A355846 A355847 A355848 * A355850 A355851 A355852

Keyword

nonn

Author

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

Status

approved