A364798 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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.

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(6) from Jinyuan Wang, Aug 09 2023

STATUS

approved