A109924 Least palindromic multiple of concatenation 123...n.

1, 252, 8118, 28382, 536797635, 6180330816, 85770307758, 2889123219882, 535841353148535, 135444949494445310, 1522312136776312132251, 2111913320628668260233191112, 6690072525779588859775252700966, 202511080654222947749222456080115202, 538412926804799527505725997408629214835

Offset: 1

Author

Amarnath Murthy, Jul 16 2005

Keywords

• nonn
• base

Comments

When n is a multiple of 10, any multiple of 123...n has trailing zeros, therefore it cannot be palindromic. The terms listed as a(10k) are therefore the least palindromic multiples with "invisible leading zeros allowed", or equivalently, trailing zeros ignored.

Subsequence of A020485.

Examples

			123*j is not palindromic for j < 66 and 123*66 = 8118, hence a(3) = 8118.
		

Links

• P. De Geest, Smallest multipliers to make a number palindromic.

Crossrefs

Cf. A020485, A050782, A061816, A109929.

Programs

Mathematica

f[n_] := Block[{k = 1, p = FromDigits[ Flatten[ IntegerDigits /@ Range[n]]]}, While[ If[ Mod[p, 10] == 0, p/=10]; While[k*p != FromDigits[ Reverse[ IntegerDigits[k*p]]], k++ ]]; k*p]; Table[ f[n], {n, 11}] (* Robert G. Wilson v, Jul 19 2005 *)

PARI

intreverse(n) = local(d, rev); rev=0; while(n>0, d=divrem(n, 10); n=d[1]; rev=10*rev+d[2]);
{s="";for(n=1,10,s=concat(s,n);k=eval(s);if(n%10==0,m=0, j=1;while((m=k*j)!=intreverse(m),j++));print1(m,","))}

PARI

A109924(n)={ n=eval(concat(vector(n,i,Str(i))));forstep(i=n/10^valuation(n,10),9e99,n/10^valuation(n,10), (m=Vec(Str(i)))==vecextract(m,"-1..1")&return(i*10^valuation(n,10)))} \\ M. F. Hasler, Jun 19 2011

Extensions

Edited and extended (a(5) to a(10)) by Klaus Brockhaus, Jul 19 2005

a(10)-a(11) from Robert G. Wilson v, Jul 19 2005

Definition of a(10k) clarified by M. F. Hasler, Jun 19 2011.

a(12)-a(14) from Giovanni Resta, Sep 22 2019

a(15) from Giovanni Resta, Sep 24 2019