A392018 Least prime p such that the sum of consecutive primes ending at p sums to a power of n > 1.

2, 3, 433, 3, 13, 7, 5, 1231, 5, 11, 7, 13, 2897, 7, 7064419, 7, 11, 19, 1801, 152953, 61, 11, 13, 103, 11, 35509, 11, 29, 17, 13, 839, 229, 101, 1097, 13, 37, 197, 13, 17579, 13, 23, 43, 2381, 15797, 149, 47, 17, 19

Offset

2,1

Links

Table of n, a(n) for n=2..49.

Carlos Rivera, Conjecture 63. Consecutive primes sum to a perfect power, The Prime Puzzles & Problems Connection.

Example

a(2) = 2 because, Sum_{i=1..1} prime(i) = 2 = 2^1.
a(3) = 3 because, Sum_{i=2..2} prime(i) = 3 = 3^1.
a(4) = 433 because, Sum_{i=5..84} prime(i) = 16384 = 4^7.
a(5) = 3 because, Sum_{i=1..2} prime(i) = 5 = 5^1.
a(6) = 13 because, Sum_{i=3..6} prime(i) = 36 = 6^2.
a(7) = 7 because, Sum_{i=4..4} prime(i) = 7 = 7^1.
a(8) = 5 because, Sum_{i=2..3} prime(i) = 8 = 8^1.
a(9) = 1231 because, Sum_{i=146..202} prime(i) = 59049 = 9^5.
a(10) = 5 because, Sum_{i=1..3} prime(i) = 10 = 10^1.
And no lesser numbers have this property.

Crossrefs

Cf. A000040, A000396, A007504, A389272.

Sequence in context: A097654 A156986 A066849 * A071219 A109855 A306370

Adjacent sequences: A392015 A392016 A392017 * A392019 A392020 A392021

Keyword

nonn,more

Author

Jean-Marc Rebert, Jan 28 2026

Status

approved