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

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.

Links

Table of n, a(n) for n=1..43.

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

Cf. A038494, A000384.

Sequence in context: A160529 A039572 A033042 * A137080 A025622 A116553

Adjacent sequences: A039591 A039592 A039593 * A039595 A039596 A039597

Keyword

nonn,base

Author

Felice Russo

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