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

1,6

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.

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

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.

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

Crossrefs

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

Sequence in context: A133843 A215083 A221308 * A221800 A291774 A222061

Adjacent sequences: A241852 A241853 A241854 * A241856 A241857 A241858

Keyword

nonn,tabl

Author

Jean-François Alcover, Apr 30 2014

Status

approved