A060433 a(n) is the smallest odd number that can be represented as the sum of one or more consecutive primes in n ways.

3, 5, 41, 1151, 311, 34421, 442019, 3634531, 48205429, 1798467197

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Sean A. Irvine, Java program (github)

Carlos Rivera, 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?, The Prime Puzzles and Problems Connection.

Example

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.

Mathematica

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 *)

Crossrefs

Sequence in context: A120265 A158328 A258933 * A216085 A219018 A191088

Adjacent sequences: A060430 A060431 A060432 * A060434 A060435 A060436

Keyword

nonn

Author

Jason Earls, Apr 06 2001

Extensions

Edited by Larry Reeves (larryr(AT)acm.org), Apr 25 2001

a(10) from Sean A. Irvine, Nov 20 2022

Status

approved