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

Author

Jon-Lark Kim, Apr 28 2013

Keywords

• nonn
• base
• easy

Examples

			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.
		

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

• Jon-Lark Kim, Preprints
• Index entries for linear recurrences with constant coefficients, signature (12,-20).

Crossrefs

Cf. A169963

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

Extensions

More terms from Colin Barker, May 11 2013