A075877 Powering the decimal digits of n (left-associative).

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 1, 6, 36, 216, 1296

Offset: 1

Author

Reinhard Zumkeller, Oct 16 2002

Keywords

• nonn
• base
• hear
• look

Comments

See A256229 for the (maybe more natural) "right-associative" variant, a(xyz)=x^(y^z). a(n) = A256229(n) for n < 212 (up to 210, according to the 2nd formula which also holds for A256229), but (2^1)^2 = 4 while 2^(1^2) = 1. - M. F. Hasler, Mar 22 2015

Examples

			a(253) = (2^5)^3 = 32^3 = 32768.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A007954.

Cf. A185969, A248907, A256179.

Programs

Haskell

a075877 n = if n < 10 then n else a075877 (n `div` 10) ^ (n `mod` 10)
-- Reinhard Zumkeller, May 27 2013

PARI

A075877(n)=if(n>9,A075877(n\10)^(n%10),n) \\ M. F. Hasler, Mar 19 2015

Formula

a(n) = if n < 10 then n else a(floor(n\10))^(n mod 10).

a(n) = 1 iff the initial digit is 1 or n contains a 0 (i.e., A055641(n) > 0 or A000030(n) = 1);

a(A011540(n)) = 1.

a(n) = A133500(n) for n <= 99. - Reinhard Zumkeller, May 27 2013

Extensions

Formula corrected by Reinhard Zumkeller, May 27 2013

Edited by M. F. Hasler, Mar 22 2015