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A174519

Sum of 3 consecutive primes and of all composite numbers in-between.

14, 25, 56, 70, 98, 112, 140, 264, 243, 297, 396, 280, 308, 528, 689, 513, 567, 726, 490, 675, 858, 924, 1350, 1235, 700, 728, 742, 770, 2242, 2318, 1452, 1215, 1859, 1885, 1377, 2041, 1782, 1848, 2249, 1593, 2405, 2431, 1358, 1372, 3060, 5275, 3723, 1582

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OFFSET

1,1

COMMENTS

2+3+4+5=14, 3+4+5+6+7=25, 5+6+7+8+9+10+11=56, ..

LINKS

Table of n, a(n) for n=1..48.

MATHEMATICA

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

sm[{a_, b_, c_}]:=(c-a+1) (a+c)/2; sm/@Partition[Prime[Range[50]], 3, 1] (* Harvey P. Dale, Mar 11 2012 *)

CROSSREFS

Cf. A034962, A054265, A174518