A129307 Intersection of A000217 and A005098.

1, 3, 10, 15, 28, 45, 78, 105, 153, 190, 253, 300, 325, 435, 465, 528, 595, 630, 780, 903, 1128, 1275, 1830, 2145, 2415, 2485, 2628, 3160, 3403, 3570, 3655, 3828, 4095, 4753, 4950, 5050, 5253, 5460, 5995, 6105, 6670, 7503, 8515, 9180, 9453, 9730, 10440, 11175

Offset: 1

Author

Zak Seidov, May 26 2007

Keywords

• nonn

Comments

Triangular numbers T(m)=m(m+1)/2 indices m of which are in A027861. T(m) such that m^2+(m+1)^2 is prime.

Crossrefs

Cf. A000217, A005098, A027861.

Programs

Maple

select(x-> isprime(4*x+1), [i*(i+1)/2$i=0..400])[];  # Alois P. Heinz, Feb 24 2024

Mathematica

Select[Table[n(n+1)/2, {n, 0, 200}], PrimeQ[4#+1]&] (* Jean-François Alcover, Feb 24 2024 *)

Formula

a(n) = A027861(n)*(A027861(n)+1)/2.

a(n) = A000217(A027861(n)).