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A109924
Least palindromic multiple of concatenation 123...n.
2
1, 252, 8118, 28382, 536797635, 6180330816, 85770307758, 2889123219882, 535841353148535, 135444949494445310, 1522312136776312132251, 2111913320628668260233191112, 6690072525779588859775252700966, 202511080654222947749222456080115202, 538412926804799527505725997408629214835
OFFSET
1,2
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.
EXAMPLE
123*j is not palindromic for j < 66 and 123*66 = 8118, hence a(3) = 8118.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Jul 16 2005
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
STATUS
approved