

A039594


Hexamorphic numbers: k such that the kth 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 kth mgonal 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*n1)); (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



