A056562 Number of primes which are the difference between two triangular numbers, where the smaller is the n-th triangular number.

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

Offset

0,3

Links

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

Formula

a(n)=2 if both n+1 is prime and 2n+3 is prime, =1 if one of n+1 and 2n+3 is prime, =0 if neither are primes.

Example

a(4)=2 because 4th triangular number is 10 and both 15-10=5 and 21-10=11 are primes.

Mathematica

npt[n_]:=Total[Boole[PrimeQ[{n+1, 2n+3}]]]; Join[{1, 1}, Array[npt, 110, 2]] (* Harvey P. Dale, Apr 30 2019 *)

Crossrefs

Cf. A000217, A001227, A056563, A056564.

Sequence in context: A112553 A026610 A094451 * A280008 A135220 A347550

Adjacent sequences: A056559 A056560 A056561 * A056563 A056564 A056565

Keyword

nonn

Author

Henry Bottomley, Jun 27 2000

Status

approved