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A039594 Hexamorphic numbers: k such that the k-th hexagonal number ends with k. 1

%I #36 Aug 19 2018 15:42:50

%S 1,5,6,25,26,50,51,75,76,125,376,500,501,625,876,4376,5000,5001,5625,

%T 9376,40625,50000,50001,59376,90625,109376,390625,500000,500001,

%U 609376,890625,2109376,2890625,5000000,5000001,7109376,7890625,12890625,37109376,50000000,50000001,62890625,87109376

%N Hexamorphic numbers: k such that the k-th hexagonal number ends with k.

%C k values for the sequence A038494.

%C These are also, whenever m == 6, 14, 30, or 38 (mod 40) the numbers k such that the k-th m-gonal number ends in k. - _Robert Dawson_, Jul 09 2018

%D D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Book, p. 104.

%D C. A. Pickover, Computers and Imagination, 1991.

%D C. A. Pickover, Hexamorphic numbers, in Hexagonal cats Ch. 63 in Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, Oxford, England: Oxford University Press, pp. 154, 2001.

%e 50 is included because the 50th hexagonal number ends with itself, i.e., 49{50}.

%t Select[Range[10^6], Mod[PolygonalNumber[6, #], 10^IntegerLength@ #] == # &] (* _Michael De Vlieger_, Jul 30 2018 *)

%o (PARI) isok(n) = {my(m = n*(2*n-1)); (m - n) % 10^#Str(n) == 0;} \\ _Michel Marcus_, Sep 25 2015

%Y Cf. A038494, A000384.

%K nonn,base

%O 1,2

%A _Felice Russo_

%E More terms from _Patrick De Geest_, Jun 15 1999

%E More terms from _Michel Marcus_, Sep 25 2015

%E Definition corrected by _Altug Alkan_, Sep 25 2015

%E Definition changed by _Robert Dawson_, Jun 20 2018

%E Name edited by _Michel Marcus_, Jul 22 2018

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)