A348790 a(n) is the smallest number that can be written as the sum of a prime number of consecutive primes in exactly n ways, or -1 if no such number exists.

1, 5, 83, 371, 311, 455713, 2196879, 77494559

Offset: 0

Author

Harvey P. Dale and N. J. A. Sloane, Nov 29 2021

Keywords

• nonn
• hard
• more

Comments

Note that a(n) itself need not be a prime (compare A348791).

Examples

			a(2) = 83 from 83 = 11+13+17+19+23 (5 primes) = 23+29+31 (3 primes).
a(3) = 371 from 371 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 (13 primes) = 41 + 43 + 47 + 53 + 59 + 61 + 67 (7 primes) = 113 + 127 + 131 (3 primes). - _Michael S. Branicky_, Nov 30 2021
a(4) = 311 from
  311 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (11 primes)
  = 31 + 37 + 41 + 43 + 47 + 53 + 59 (7 primes)
  = 53 + 59 + 61 + 67 + 71 (5 primes)
  = 101 + 103 + 107 (3 primes).
The 7 ways to get a(7), written as [count, first prime in sum, last prime in sum, # of primes in sum]: [1, 233, 39551, 4111], [2, 42323, 58909, 1531], [3, 135899, 142381, 557], [4, 710321, 711691, 109], [5, 1061087, 1062073, 73], [6, 4558349, 4558633, 17], [7, 15498871, 15498971, 5]. - _Hugo Pfoertner_, Nov 30 2021
		

Crossrefs

Cf. A082283. See A348791 for another version.

Extensions

a(6)-a(7) from Hugo Pfoertner, Nov 30 2021

a(3) and a(5) corrected by Michael S. Branicky, Nov 30 2021