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A056562
Number of primes which are the difference between two triangular numbers, where the smaller is the n-th triangular number.
2
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
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jun 27 2000
STATUS
approved