

A171775


a(n) = smallest number M such that there exist bases b_2, b_3, ..., b_n with the property that M written in base b_k is a kdigit palindrome for all k=2..n.


15




OFFSET

1,2


COMMENTS

a(n) is no more than 2^[(n1)*(n2)] for n > 6 (and equals it for n = 7 and 8 at least). The reason for this bound is that for this number for each length from n down to 3 there is at least one power of 2, 2^k, such that in base b = 2^k1 the binomial expansion of (b+1)^floor([(n1)*(n2)]/k) multiplied by the remaining small power of 2 gives a palindromic expression not requiring carries in base b. James G. Merickel, Aug 05 2015


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

a(6)=1885: the bases are 1884 (1885 is 11 in base 1884), 14 (1885 is 989 in base 14), 12 (it is 1111 in base 12), 6 (it is 12421 in base 6), and 4 (it is 131131 in base 4).


CROSSREFS

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165, A087155, A171701, A171702, A171703, A171704, A171705, A171706, A171740, A171741, A171742, A253294.
Sequence in context: A077201 A196467 A219506 * A260227 A260226 A101149
Adjacent sequences: A171772 A171773 A171774 * A171776 A171777 A171778


KEYWORD

nonn,base,hard,more


AUTHOR

James G. Merickel, Dec 18 2009


EXTENSIONS

a(7) and a(8) added by James G. Merickel, Feb 04 2010
Offset changed to 1, with corresponding addition of a(1) by James G. Merickel, Jul 24 2015
Comment corrected and explained.James G. Merickel, Aug 05 2015
Definition and example rewritten by N. J. A. Sloane, Aug 05 2015


STATUS

approved



