A340883 Row sums of A340882.

1, 5, 91, 6245, 1658011, 1729699685, 7151839686811, 117731539542445925, 7733983187987903246491, 2029827406487942179094302565, 2129693923358322199845305015300251, 8935240067815150709523569975709449359205

Offset

1,2

Comments

Conjectures:

1) The sequence taken modulo n becomes periodic with a pre-period of length either 0 or 1, and with the minimum period dividing phi(n). For example, taken modulo 21 the sequence becomes [1, 5, 7, 8, 19, 14, 1, 5, 7, 8, 19, 14, ...], apparently a purely periodic sequence of period 6.

2) If n and m are coprime then the period of the sequence taken modulo n*m equals the l.c.m. of the periods of the sequence taken modulo n and taken modulo m.

Links

Table of n, a(n) for n=1..12.

Formula

a(n) = Sum_{k = 0..n-1} 2^(k^2) * ( Product_{j = k+1..n-1} 2^(2*j) - 1 ).

Maple

a := n -> add( 2^(k^2)*mul(2^(2*j)-1, j = k+1 .. n-1), k = 0..n-1 ):
seq(a(n), n = 1..20);

Crossrefs

Cf. A340880, A340881, A340882.

Sequence in context: A343009 A368776 A340052 * A109625 A266290 A348347

Adjacent sequences: A340880 A340881 A340882 * A340884 A340885 A340886

Keyword

nonn,easy

Author

Peter Bala, Feb 16 2021

Status

approved