|
%I #17 Jun 22 2018 02:48:40
%S 1,7,17,51,67,167,251,417,501,667,751,917,1251,1667,5001,5417,6251,
%T 6667,10417,16667,50001,56251,60417,66667,166667,260417,406251,500001,
%U 666667,760417,906251,1406251,1666667,5000001,5260417,6406251,6666667,16666667
%N Centered hexamorphic numbers: the k-th centered hexagonal number, 3k(k-1)+1, ends in k.
%C 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.
%H Robert Munafo, <a href="http://www.mrob.com/pub/math/seq-a094534.html">Sequence A094534, Centered Hexamorphic, or Automorphic Hexagonal, Numbers</a>
%H Cliff Pickover, <a href="http://sprott.physics.wisc.edu/pickover/clifft.html">Centered Hexamorphic Numbers</a>.
%F 10^(d-1) <= n < 10^d; 3n(n-1)+1 == n mod 10^d
%e 417 is in the sequence because if n=417, 3n(n-1)+1=520417, which ends in 417.
%o (PARI) isok(n) = {my(m = 3*n*(n-1)+1); (m - n) % 10^#Str(n) == 0; } \\ _Michel Marcus_, Jun 21 2018
%Y Cf. A003215, A003226.
%K base,easy,nonn
%O 1,2
%A _Robert Munafo_, May 07 2004
%E Name changed by _Robert Dawson_, Jun 20 2018
|
