A078211 Smallest multiple of n^2 beginning and ending in n, or 0 if no such multiple exists.

1, 212, 333, 464, 525, 6156, 7007, 8128, 9639, 0, 11011, 122112, 13013, 0, 0, 162816, 1720417, 0, 1905719, 0, 212121, 0, 2320723, 244224, 25625, 0, 2743227, 287728, 2917429, 0, 3143431, 325632, 3372633, 0, 0, 3617136, 373737, 0, 393939, 0, 4136941

Offset

1,2

Links

Table of n, a(n) for n=1..41.

Prog

(PARI) { a(n) = local(l, m); l=#Str(n); m=valuation(n, 2); if(m>0 && m<l, return(0)); m=valuation(n, 5); if(m>0 && m<l, return(0)); for(j=0, l-1, if(n%10^(l-j)==n\10^j && (n*10^j + n%10^j)%n^2==0, return(n*10^j + n%10^j)); ); if((10^l+1)%n==0, return(n*(10^l+1))); m=0; g=gcd(n^2, 10^l); until(#Str(t)<=m, m++; t=lift(Mod(-n*(10^(m+l)+1)/g, n^2/g)/(10^l\g)); ); n*(10^(m+l)+1)+t*10^l } \\ Max Alekseyev, Oct 18 2008

Crossrefs

Cf. A078208, A077209, A077210, A078212.

Sequence in context: A093807 A088642 A251126 * A158794 A204364 A235180

Adjacent sequences: A078208 A078209 A078210 * A078212 A078213 A078214

Keyword

base,nonn

Author

Amarnath Murthy, Nov 22 2002

Extensions

a(11) and up from Max Alekseyev, Oct 18 2008

Status

approved