A364798 Triangular numbers that for some k >= 1 are also the sum of the first k noncomposite numbers (1 together with the primes).

1, 3, 6, 78, 448516225, 448254714630193471

Offset

1,2

Comments

a(n) = A000217(i) = A014284(j) for appropriate i, j.

Links

Table of n, a(n) for n=1..6.

Example

78 is a term because 78 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 1 + 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19.

Mathematica

Select[Accumulate[Join[{1}, Prime[Range[10000]]]], IntegerQ[Sqrt[8 # + 1]] &]

Crossrefs

Intersection of A000217 and A014284.

Cf. A008578, A066527, A110996, A364799.

Sequence in context: A023174 A350992 A213138 * A349875 A331403 A357245

Adjacent sequences: A364795 A364796 A364797 * A364799 A364800 A364801

Keyword

nonn,more

Author

Ilya Gutkovskiy, Aug 08 2023

Extensions

a(6) from Jinyuan Wang, Aug 09 2023

Status

approved