A116943 Number of 4s digits plus non-final 3s digits 3 base 5 expansion of 2^n.

0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 3, 2, 2, 2, 1, 1, 3, 4, 5, 3, 3, 1, 4, 4, 7, 2, 7, 7, 4, 6, 9, 9, 6, 5, 5, 7, 4, 9, 4, 7, 7, 7, 10, 8, 6, 8, 6, 9, 8, 9, 8, 10, 11, 11, 8, 13, 5, 11, 15, 13, 10, 10, 8, 12, 9, 14, 11, 8, 11, 12, 10, 13, 13, 13, 10, 10, 12, 6, 10, 15, 8, 17, 17, 16, 16, 12, 16, 15, 13

Offset: 0

Author

Jonathan Vos Post, Mar 23 2006

Keywords

• base
• easy
• nonn

Comments

In his comment on A038003 Frank Adams-Watters conjectures "that 2^n contains such a base 5 digit for n>=9. This is almost certainly true." That is equivalent to a(n) > 0 for n>=9, which is also equivalent to A094389(n) = 5 where A094389 is last decimal digit of the odd Catalan number A038003(n).

Examples

			a(7) = 0 because 2^7 (modulo 5) = 1003, which contains 0 digits 4 plus 0 non-final digits 3 (it has a digit 3, but that digit is finial, meaning rightmost).
a(10) = 3 because 2^10 mod 5 = 13044, which contains 2 digits 4 plus 1 non-final digits 3, so 2 + 1 = 3.
a(60) = 10 because 2^60 mod 5 = 34132411211412413323100401, which contains 5 digits 4 plus 5 non-final digits 3, so 5 + 5 = 10.
		

Crossrefs

Cf. A038003, A094389.

Programs

Mathematica

f[n_] := Block[{id = IntegerDigits[2^n, 5]}, Count[id, 4] + Count[Most@id, 3]]; Table[ f[n], {n, 0, 88}] (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v, Apr 01 2006