A231118 Numbers n such that n*91^k is palindromic for k=0,...,4

14641, 147741, 1478741, 14788741, 146424641, 147767741, 147888741, 1464114641, 1476226741, 1477557741, 1478778741, 1478888741, 1489779841, 14641014641, 14762026741, 14774247741, 14775457741, 14787678741, 14788888741, 14883038841, 14895259841, 14896469841

Offset

1,1

Comments

Necessarily a subsequence of A002113.

It is an open question whether there exists a,r>1 such that a*r^k is palindromic for k=0,...,5.

There is no n with n*91^k palindromic for k=0..5 with n < 10^17. - Charles R Greathouse IV, Nov 05 2013

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..250

West Coast Number Theory, WCNT Problem sets 2012, problem 012.07.

Prog

(PARI) ispal(n)=my(v=digits(n)); for(i=1, #v\2, if(v[i]!=v[#v+1-i], return(0))); 1
has(n)=for(k=1, 4, if(!ispal(n*=91), return(0))); 1
u=List(); for(n=1, 10^5-1, for(m=-1, 9, v=digits(n); v=if(m<0, concat(v, Vecrev(v)), concat(concat(v, m), Vecrev(v))); N=subst(Pol(v), x, 10); if(has(N), listput(u, N)))); Set(u) \\ Charles R Greathouse IV, Nov 04 2013

Crossrefs

Sequence in context: A252218 A133858 A023683 * A017284 A017392 A017656

Adjacent sequences: A231115 A231116 A231117 * A231119 A231120 A231121

Keyword

nonn,base

Author

M. F. Hasler, Nov 04 2013

Status

approved