A174518 Sums of two consecutive primes and composite numbers in-between.

5, 12, 18, 45, 36, 75, 54, 105, 182, 90, 238, 195, 126, 225, 350, 392, 180, 448, 345, 216, 532, 405, 602, 837, 495, 306, 525, 324, 555, 1800, 645, 938, 414, 1584, 450, 1078, 1120, 825, 1190, 1232, 540, 2046, 576, 975, 594, 2665, 2821, 1125, 684, 1155, 1652

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 21 2010

Keywords

• nonn

Crossrefs

Cf. A034962, A054265.

Programs

Mathematica

f[n_,x_]:=n*x+x*(x+1)/2;Table[Prime[n]+f[Prime[n],Prime[n+1]-Prime[n]-1]+Prime[n+1],{n,5!}]

Formula

a(n) = Sum_{k=prime(n)..prime(n+1)} k. - Wesley Ivan Hurt, Apr 27 2021