A056563 - OEIS

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A056563

Number of primes which are the difference between two triangular numbers, where the larger is the n-th triangular number.

0, 0, 1, 2, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..104.

EXAMPLE

a(7)=2 because 7th triangular number is 28 and both 28-21=7 and 28-15=13 are primes.

MATHEMATICA

Join[{0}, Table[With[{tr=Accumulate[Range[n]]}, Count[tr[[-1]]-Most[tr], _?PrimeQ]], {n, 120}]] (* Harvey P. Dale, Mar 31 2023 *)

CROSSREFS

Cf. A000217, A001227, A056562, A056564.

Sequence in context: A292378 A320835 A276183 * A088231 A327954 A336386