A197227 Primes that are not the sum of at least two consecutive primes.

2, 3, 7, 11, 13, 19, 29, 37, 43, 47, 61, 73, 79, 89, 103, 107, 113, 137, 149, 151, 157, 163, 167, 179, 191, 193, 227, 229, 239, 241, 257, 277, 283, 293, 307, 313, 317, 337, 347, 359, 367, 383, 389, 397, 409, 419, 433, 461, 467, 509, 521, 541, 547, 557, 569

Offset: 1

Author

T. D. Noe, Nov 03 2011

Keywords

• nonn

Comments

Complement of A067377 in the primes. For the primes less than 10^6, these primes make up about 56%.

Links

• Robert Israel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A050940, A067377, A307610.

Programs

Maple

P:= [seq(ithprime(i),i=1..10^3)]:
S:= ListTools:-PartialSums([0,op(P)]):
sort(convert(convert(P,set) minus {seq(seq(S[i]-S[j],j=1..i-2),i=1..10^3+1)},list)); # Robert Israel, May 09 2021

Mathematica

lim = 1000; pFound = {}; 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[PrimeQ[sm[[j]]], AppendTo[pFound, sm[[j]]]]; j++]; j > 1]; Complement[ps, pFound]

Formula

Prime(n) such that A307610(n) = 1. - Ray Chandler, Sep 21 2023

Extensions

Definition clarified by Jonathan Sondow, May 18 2013