A337261 Numbers k such that the digits of 4^k cannot be rearranged to form the digits of t^2, for t not a power of 2.

0, 1, 2, 3, 8, 9, 11, 12

Offset: 1

Author

N. J. A. Sloane, Aug 22 2020

Keywords

• nonn
• base
• more

Comments

Leading zeros are not allowed.

2^odd cannot be rearranged to a square number: odd powers of 2 are congruent to 2,5,8 mod 9; squares are congruent to 0,1,4,7 mod 9; and rearranging preserves the mod-9 value.

If it exists, a(9) > 78.

Examples

			4 is not here because 4^4 = 256 -> 625 = 25^2.
10 is not here, because 4^10 = 1048576 -> 1056784 = 1028^2.
11 is here, even though 4^11 = 4194304 -> 0413449 = 643^2, because leading zeros aren't allowed.
		

References

• Don Reble, Posting to Sequence Fans Mailing List, Aug 21 2020

Crossrefs

Cf. A000302 (powers of 4), A337252.