A340537 Primes that are sums of a sequence of consecutive terms of A006094.

127, 491, 1201, 1427, 2003, 2713, 2767, 5431, 7229, 7639, 13001, 17231, 18061, 20753, 24509, 37337, 37589, 38149, 38261, 44563, 44839, 50969, 51517, 53609, 55201, 60859, 76519, 77191, 80239, 80783, 81703, 90823, 91583, 96493, 103079, 103687, 110573, 126713, 130411, 134093, 137777, 139199, 139663

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 10 2021

Keywords

• nonn

Comments

Each term is the sum of at least three consecutive terms of A006094.

A number that can be expressed as such a sum in more than one way is only listed once. The first such number is 50911291 = 547*557+...+1051*1061 = 1423*1427+...+1559*1567.

Examples

			a(1) = 5*7+7*11+11*13 = 127.
a(2) = 5*7+7*11+11*13+13*17+17*19 = 491.
a(3) = 11*13+13*17+17*19+19*23+23*29 = 1201.
a(4) = 19*23+23*29+29*31 = 1427.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006094, A340465. Includes A287653.

Programs

Maple

SP:= [seq(ithprime(i)*ithprime(i+1),i=1..100)]:
SSP:= ListTools:-PartialSums([0,op(SP)]):
select(t -> t <= SP[-1] and isprime(t),
  {seq(seq(SSP[j]-SSP[i],i=1..j-3),j=4..nops(SSP))});