A337095 Prime numbers that can be expressed as the sum of k>1 consecutive prime numbers in only one way.

5, 17, 23, 31, 53, 59, 67, 71, 97, 101, 109, 127, 131, 139, 173, 181, 211, 233, 263, 269, 271, 331, 349, 353, 373, 379, 421, 431, 443, 449, 457, 463, 479, 487, 499, 503, 523, 563, 587, 607, 617, 631, 647, 659, 661, 677, 683, 691, 701, 719, 757, 787, 797, 811, 827, 829, 839

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 15 2020

Keywords

• nonn

Examples

			a(1) = 5 is the sum of k>1 consecutive primes in exactly one way: 5 = 2+3;
a(2) = 17 is the sum of k>1 consecutive primes in exactly one way: 17 = 2+3+5+7;
a(3) = 23 is the sum of k>1 consecutive primes in exactly one way: 23 = 2+3+5+7+11;
a(4) = 31 is the sum of k>1 consecutive primes in exactly one way: 31 = 7+11+13;
a(5) = 53 is the sum of k>1 consecutive primes in exactly one way: 53 = 5+7+11+13+17; etc.
The prime number 41 is not in the sequence because 41 is the sum of k>1 consecutive primes in more than one way: 41 = 2+3+5+7+11+13 and 41 = 11+13+17.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 354 terms from Jean-Marc Falcoz)

Crossrefs

Cf. A084146.

Formula

A084146 INTERSECT A000040. - R. J. Mathar, Aug 19 2020