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