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

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

Adjacent sequences: A056560 A056561 A056562 * A056564 A056565 A056566

Keyword

nonn

Author

Henry Bottomley, Jun 27 2000

Extensions

Formula deleted by Harvey P. Dale, Mar 31 2023

Status

approved