A174245 a(n) is the smallest number m such that the sum of the first m squares ends in n '0's.

4, 24, 624, 5312, 45312, 445312, 6445312, 12890624, 212890624, 893554687, 40893554687, 40893554687, 81787109375, 59918212890624, 129959106445312, 3740081787109375, 56259918212890624, 128129959106445312, 3871870040893554687, 7743740081787109375, 607743740081787109375

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..997

Example

The smallest sum of squares ending in a zero is 1^2 + 2^2 + 3^2 + 4^2 = 30, so a(1)=4. Likewise, 1^2 + ... + 24^2 = 4900, so a(2)=24.

Maple

f:= n -> min(map(rhs@op, {msolve(k*(k+1)*(2*k+1), 6*10^n)}) minus {0}):
map(f, [$1..30]); # Robert Israel, Mar 13 2025

Prog

(PARI) sos(x) = x*(x+1)*(2*x+1)/6;
a(n)={ local(s5=polrootspadic(sos(x), 5, n), s2=polrootspadic(sos(x), 2, n), ss10=Set()); for(i2=1, length(s2), v2=lift(s2[i2]); if(denominator(v2)==1, m2=Mod(v2, 2^n); for(i5=1, length(s5), s10=lift(chinese(m2, Mod(s5[i5], 5^n))); if(s10!=0&&sos(s10)%(10^n)==0, ss10=setunion(ss10, Set(s10))) ) ) ); ss10[1] }

Crossrefs

Cf. A000330.

Sequence in context: A249028 A394097 A216092 * A228191 A012989 A347480

Adjacent sequences: A174242 A174243 A174244 * A174246 A174247 A174248

Keyword

nonn,base

Author

Phil Carmody, Mar 13 2010

Extensions

Typo in definition corrected by Zak Seidov, Mar 16 2010

a(10) corrected by and more terms from Jinyuan Wang, Aug 23 2021

Status

approved