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
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.
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
Comments