A115783 Numbers that can be represented in the form (m+1)^k - m^k in at least two ways.

0, 1, 7, 15, 19, 31, 37, 61, 63, 65, 91, 127, 169, 175, 211, 217, 255, 271, 331, 369, 397, 469, 511, 547, 631, 665, 671, 721, 781, 817, 919, 1023, 1027, 1105, 1141, 1261, 1387, 1519, 1657, 1695, 1801, 1951, 2047, 2059, 2101, 2107, 2269, 2437, 2465, 2611, 2791

Offset

1,3

Comments

It is easy to see that all the terms of A003215 also belong to this sequence (thus infinite), since they can be represented as (p+1)^2 - p^2 and as (q+1)^3 - q^3. - Giovanni Resta, Feb 15 2006

Links

Table of n, a(n) for n=1..51.

Mathematica

t = {}; Do[a = (m + 1)^k - m^k; If[a < 3000, AppendTo[t, a]], {m, 3000}, {k, 23}]; t = Split@ Sort@ t; Union@ Flatten@ t[[Select[ Range@1500, Length@t[[ # ]] > 1 &]]] (* Robert G. Wilson v, Feb 08 2006 *)

Crossrefs

Sequence in context: A138641 A297853 A298050 * A140109 A064397 A214467

Adjacent sequences: A115780 A115781 A115782 * A115784 A115785 A115786

Keyword

nonn

Author

Zak Seidov, Jan 30 2006

Extensions

Corrected and extended by Robert G. Wilson v, Feb 08 2006

Corrected and extended by Giovanni Resta, Feb 15 2006

Status

approved