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

1,1

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.

Links

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

Example

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.

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))});

Crossrefs

Cf. A006094, A340465. Includes A287653.

Sequence in context: A129537 A057814 A038646 * A245867 A096523 A299132

Adjacent sequences: A340534 A340535 A340536 * A340538 A340539 A340540

Keyword

nonn

Author

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

Status

approved