A376614 a(n) is the least n-gonal number that is an interprime, i.e. the average of two consecutive primes.

6, 4, 12, 6, 18, 21, 9, 370, 30, 12, 405, 39, 15, 45, 231, 18, 2619, 2772, 21, 205, 596, 69, 72, 26, 154, 81, 574, 30, 441, 93, 315, 34, 102, 105, 108, 111, 39, 1377, 120, 42, 1485, 129, 45, 1990, 138, 465, 144, 50, 150, 4564, 515, 19684, 1120, 56, 334, 846, 861, 60, 180, 5474, 186, 64, 192, 195

Offset: 3

Author

Robert Israel, Sep 29 2024

Keywords

• nonn

Comments

a(n) is the first number of the form ((n-2)*k^2 - (n-4)*k)/2 for k >= 0 that is in A024675.

a(n) = n if n is in A024675.

Examples

			a(5) = 12 because 12 = A000326(3) is a pentagonal number and is the average of consecutive primes 11 and 13, and neither of the previous pentagonal numbers (1 and 5) are averages of consecutive primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A024675, A000326, A086270.

Programs

Maple

f:= proc(s) local n,x;
   for n from 1 do
     x:= ((s-2)*n^2 - (s-4)*n)/2;
     if x >= 4 and not isprime(x) and prevprime(x) + nextprime(x) = 2*x then return x fi
   od
end proc:
map(f, [$3..100]);