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Search: id:A115783
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| A115783 |
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Numbers n such that n can be presented in the form (m+1)^k-m^k at least in two ways. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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It is easy to see that all the members 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 (g.resta(AT)iit.cnr.it), Feb 15 2006
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MATHEMATICA
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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
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CROSSREFS
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Sequence in context: A065566 A154618 A138641 this_sequence A140109 A064397 A151971
Adjacent sequences: A115780 A115781 A115782 this_sequence A115784 A115785 A115786
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Jan 30 2006
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v, Feb 08 2006
Corrected and extended by Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 15 2006
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