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

Offset: 1

Author

Robert Munafo, May 07 2004

Keywords

• base
• easy
• nonn

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.

Examples

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

Links

• Robert Munafo, Sequence A094534, Centered Hexamorphic, or Automorphic Hexagonal, Numbers
• Cliff Pickover, Centered Hexamorphic Numbers.

Crossrefs

Cf. A003215, A003226.

Programs

PARI

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

Formula

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

Extensions

Name changed by Robert Dawson, Jun 20 2018