|
%I #24 Nov 20 2022 08:15:15
%S 3,5,41,1151,311,34421,442019,3634531,48205429,1798467197
%N a(n) is the smallest odd number that can be represented as the sum of one or more consecutive primes in n ways.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a060/A060433.java">Java program</a> (github)
%H Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_009.htm">Problem 9. Let f(n) be the number of ways of representing n as the sum of one or more consecutive primes. Is f(n)=k solvable for every k?</a>, The Prime Puzzles and Problems Connection.
%e a(2) = 5 because of 5 and 2+3 = 5. a(3) = 41 because of 41, 2+3+5+7+11+13 = 41 and 11+13+17 = 41.
%t lim = 500000; cnt = Table[If[OddQ[n] && PrimeQ[n], 1, 0], {n, lim}]; ps = Prime[Range[PrimePi[lim]]]; sm = ps; i = 0; While[i++; j = 1; While[sm[[j]] = sm[[j]] + ps[[i + j]]; sm[[j]] <= lim, If[OddQ[sm[[j]]], cnt[[sm[[j]]]]++]; j++]; j > 1]; Table[Position[cnt, i, 1, 1][[1, 1]], {i, Union[cnt][[-1]]}] (* _T. D. Noe_, Nov 03 2011 *)
%K nonn
%O 1,1
%A _Jason Earls_, Apr 06 2001
%E Edited by Larry Reeves (larryr(AT)acm.org), Apr 25 2001
%E a(10) from _Sean A. Irvine_, Nov 20 2022
|
