A241855 Array t(n,k) of sum of successive even powers of primes, where t(n,k) = sum_(j=0..k-1) prime(n)^(2j), with n>=1 and k>=0, read by ascending antidiagonals.

0, 0, 1, 0, 1, 5, 0, 1, 10, 21, 0, 1, 26, 91, 85, 0, 1, 50, 651, 820, 341, 0, 1, 122, 2451, 16276, 7381, 1365, 0, 1, 170, 14763, 120100, 406901, 66430, 5461, 0, 1, 290, 28731, 1786324, 5884901, 10172526, 597871, 21845, 0, 1, 362, 83811, 4855540, 216145205, 288360150, 254313151, 5380840, 87381

Offset: 1

Author

Jean-François Alcover, Apr 30 2014

Keywords

• nonn
• tabl

Comments

Conjecture: any term, except 0 and 1, is never a square.

Row n=1 is A002450,

row n=2 is A002452,

row n=3 is A218728,

row n=4 is A218753,

rows n>=5 are not in the OEIS,

column k=2 is A066872,

columns k>=3 are not in the OEIS.

Examples

			Array begins:
0,  1,   5,    21,      85,       341,        1365, ...
0,  1,  10,    91,     820,      7381,       66430, ...
0,  1,  26,   651,   16276,    406901,    10172526, ...
0,  1,  50,  2451,  120100,   5884901,   288360150, ...
0,  1, 122, 14763, 1786324, 216145205, 26153569806, ...
etc.
		

Crossrefs

Cf. A002450, A002452, A066872, A059826, A059830, A059839, A218728, A218753.

Programs

Mathematica

t[n_, k_] := ((Prime[n]^2)^k-1)/(Prime[n]^2-1); Table[t[n-k+1, k], {n, 0, 10}, {k, 0, n}] // Flatten

Formula

t(n,k) = ((prime(n)^2)^k-1)/(prime(n)^2-1).