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A039594
Hexamorphic numbers: k such that the k-th hexagonal number ends with k.
1
1, 5, 6, 25, 26, 50, 51, 75, 76, 125, 376, 500, 501, 625, 876, 4376, 5000, 5001, 5625, 9376, 40625, 50000, 50001, 59376, 90625, 109376, 390625, 500000, 500001, 609376, 890625, 2109376, 2890625, 5000000, 5000001, 7109376, 7890625, 12890625, 37109376, 50000000, 50000001, 62890625, 87109376
OFFSET
1,2
COMMENTS
k values for the sequence A038494.
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
REFERENCES
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Book, p. 104.
C. A. Pickover, Computers and Imagination, 1991.
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.
EXAMPLE
50 is included because the 50th hexagonal number ends with itself, i.e., 49{50}.
MATHEMATICA
Select[Range[10^6], Mod[PolygonalNumber[6, #], 10^IntegerLength@ #] == # &] (* Michael De Vlieger, Jul 30 2018 *)
PROG
(PARI) isok(n) = {my(m = n*(2*n-1)); (m - n) % 10^#Str(n) == 0; } \\ Michel Marcus, Sep 25 2015
CROSSREFS
Sequence in context: A160529 A039572 A033042 * A137080 A025622 A116553
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
More terms from Patrick De Geest, Jun 15 1999
More terms from Michel Marcus, Sep 25 2015
Definition corrected by Altug Alkan, Sep 25 2015
Definition changed by Robert Dawson, Jun 20 2018
Name edited by Michel Marcus, Jul 22 2018
STATUS
approved