A225107 Number of (4n-3)-digit 4th powers in carryless arithmetic mod 10.

3, 24, 228, 2256, 22512, 225024, 2250048, 22500096, 225000192, 2250000384, 22500000768, 225000001536, 2250000003072, 22500000006144, 225000000012288, 2250000000024576, 22500000000049152, 225000000000098304, 2250000000000196608, 22500000000000393216

Offset

1,1

References

J. Y. Lee and J.-L. Kim, Powers, Pythagorean triples, and Fermat's Last Theorem in carryless arithmetic mod 10, preprint, April, 18, 2013.

Links

Table of n, a(n) for n=1..20.

Jon-Lark Kim, Preprints

Index entries for linear recurrences with constant coefficients, signature (12,-20).

Formula

a(k) = (1/4)*{9* 10^(k-1) - 2^(k-1)} + 2^(k-1).

a(n) = 12*a(n-1)-20*a(n-2). G.f.: -3*x*(4*x-1) / ((2*x-1)*(10*x-1)). - Colin Barker, May 11 2013

Example

For k=1, there are three one-digit 4th powers: 1^4=9^4=3^4=7^4=1, 2^4=8^4=4^4=6^4=6, 5^4=5.

Crossrefs

Cf. A169963

Sequence in context: A274737 A324446 A307514 * A249926 A279651 A001099

Adjacent sequences: A225104 A225105 A225106 * A225108 A225109 A225110

Keyword

nonn,base,easy

Author

Jon-Lark Kim, Apr 28 2013

Extensions

More terms from Colin Barker, May 11 2013

Status

approved