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

1,2

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.

Links

Table of n, a(n) for n=1..48.

Formula

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

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

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 *)

Crossrefs

Cf. A000217, A005098, A027861.

Sequence in context: A325233 A030005 A192163 * A186575 A356318 A233312

Adjacent sequences: A129304 A129305 A129306 * A129308 A129309 A129310

Keyword

nonn

Author

Zak Seidov, May 26 2007

Status

approved