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

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

Offset

1,2

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

Table of n, a(n) for n=1..15.

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, Jul 19 2005 *)

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