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A094534

Centered hexamorphic numbers: the k-th centered hexagonal number, 3k(k-1)+1, ends in k.

1, 7, 17, 51, 67, 167, 251, 417, 501, 667, 751, 917, 1251, 1667, 5001, 5417, 6251, 6667, 10417, 16667, 50001, 56251, 60417, 66667, 166667, 260417, 406251, 500001, 666667, 760417, 906251, 1406251, 1666667, 5000001, 5260417, 6406251, 6666667, 16666667

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OFFSET

1,2

COMMENTS

Given any number in the sequence, if you remove one or more digits from the beginning you always get another number in the sequence. This makes it easy to find higher terms -- just take an existing term and try adding a digit (with perhaps additional 0's) at the beginning. For example, to 6251 prepend 5 to get a 5-digit term, or 40 or 90 to get a 6-digit term.

LINKS

Table of n, a(n) for n=1..38.

Robert Munafo, Sequence A094534, Centered Hexamorphic, or Automorphic Hexagonal, Numbers

Cliff Pickover, Centered Hexamorphic Numbers.

FORMULA

10^(d-1) <= n < 10^d; 3n(n-1)+1 == n mod 10^d

EXAMPLE

417 is in the sequence because if n=417, 3n(n-1)+1=520417, which ends in 417.

PROG

(PARI) isok(n) = {my(m = 3*n*(n-1)+1); (m - n) % 10^#Str(n) == 0; } \\ Michel Marcus, Jun 21 2018

CROSSREFS

Cf. A003215, A003226.