A067372 Integers expressible as the sum of (at least two) consecutive primes in at least 2 ways.

36, 41, 60, 72, 83, 90, 100, 112, 119, 120, 138, 143, 152, 180, 187, 197, 199, 204, 210, 221, 223, 228, 240, 251, 258, 276, 281, 287, 300, 304, 311, 323, 330, 340, 371, 372, 384, 390, 395, 401, 408, 410, 434, 439, 456, 462, 473, 480, 491, 492, 508, 510, 533

Offset: 1

Author

Patrick De Geest, Feb 04 2002

Keywords

• nonn
• easy

Examples

			36 = (17 + 19) = (5 + 7 + 11 + 13) or (#2,17) (#4,5).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10841 (terms <= 10^5, first 1000 terms from Donovan Johnson)
• P. De Geest, WONplate 122
• C. Rivera, Puzzle 46
• Eric Weisstein's World of Mathematics, Prime Sums

Crossrefs

Cf. A050936, A067372-A067381, A054997.

Programs

Mathematica

m=5!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[pVladimir Joseph Stephan Orlovsky, Aug 15 2009 *)

PARI

upto(n) = {my(s = 0, pr = List([0]), l = List(), res = List()); forprime(p = 2, n + 100, s+=p; listput(pr, s) ); for(i = 3, #pr, for(j = 2, i-1, if(pr[i] - pr[i-j] <= n, listput(l, pr[i] - pr[i-j]) , next(2) ) ) ); listsort(l); for(i = 2, #l, if(l[i-1] == l[i], listput(res, l[i]) ) ); Set(res); } \\ David A. Corneth, Aug 22 2019

Formula

A084143(a(n)) > 1. - Ray Chandler, Sep 20 2023

Extensions

Offset corrected by Donovan Johnson, Nov 14 2013