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%I #15 Aug 14 2021 18:54:56
%S 0,1,7,15,19,31,37,61,63,65,91,127,169,175,211,217,255,271,331,369,
%T 397,469,511,547,631,665,671,721,781,817,919,1023,1027,1105,1141,1261,
%U 1387,1519,1657,1695,1801,1951,2047,2059,2101,2107,2269,2437,2465,2611,2791
%N Numbers that can be represented in the form (m+1)^k - m^k in at least two ways.
%C 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
%t 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 *)
%K nonn
%O 1,3
%A _Zak Seidov_, Jan 30 2006
%E Corrected and extended by _Robert G. Wilson v_, Feb 08 2006
%E Corrected and extended by _Giovanni Resta_, Feb 15 2006