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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS P. De Geest, Smallest multipliers to make a number palindromic. 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 *) PROG (PARI) {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, ", "))} (for intreverse see A067723) (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 Cf. A020485, A050782, A061816, A109929. Sequence in context: A177301 A250376 A329755 * A281032 A047831 A076013 Adjacent sequences:  A109921 A109922 A109923 * A109925 A109926 A109927 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

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Last modified April 8 23:02 EDT 2020. Contains 333331 sequences. (Running on oeis4.)