A060341 Non-adding primes: next term is smallest prime not the sum of any primes so far.

2, 3, 7, 11, 17, 41, 47, 83, 89, 307, 311, 613, 617, 919, 2801, 3109, 3413, 9283, 15461, 25087, 37781, 87613, 106181, 284509, 296591, 618269, 1196609, 1774921, 3564677, 5339287, 9818789, 14295223, 23196731, 46393469, 93691861, 98171363, 190948399, 429204473

Offset

1,1

Comments

Primes can only be used once in any sum.

Links

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Carlos Rivera, Puzzle 127. Non adding prime sequences, The Prime Puzzles & Problems Connection.

Example

5 is not included because 2 + 3 = 5. Given 2, 3, 7 we can get 5 but not 11, so term after 7 is 11.
13 is not included because 2 + 11 = 13.

Prog

(PARI) lista(nn) = my(p=2, i, j, s, t, u, v=[2, 1], w); print1(p); for(n=2, nn, u=0; i=1; j=1; w=List([]); s=0; t=1; while(i<=#v, if(j>#v, if(i%2==t, s+=v[i], t=!t; listput(w, s); s=v[i]); i++, if(v[i]>u, if((i%2&&j%2)==t, s+=u, t=!t; listput(w, s); s=u); v[i]-=u; if(j++<=#v, u=v[j]), if((i%2&&j%2)==t, s+=v[i], t=!t; listput(w, s); s=v[i]); if(v[i]==u, if(j++<=#v, u=v[j]), u-=v[i]); i++))); listput(w, s); v=w; s=0; i=0; until(isprime(p), p++; while(s<=p&&i<#v, s+=v[i++]); if(s>p&&!(i%2), p=s)); print1(", ", v[1]=p)); \\ Jinyuan Wang, Dec 17 2024

Crossrefs

Cf. A225947, A379045.

Sequence in context: A330070 A350839 A161921 * A114345 A077165 A090666

Adjacent sequences: A060338 A060339 A060340 * A060342 A060343 A060344

Keyword

nonn

Author

Jason Earls, Apr 10 2001

Extensions

a(37)-a(53) from Jacques Tramu, Jan 11 2005

Offset changed to 1 by Jinyuan Wang, Dec 17 2024

Status

approved