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A075877 Powering the decimal digits of n (left-associative). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

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

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

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A007953, A007954.

Cf. A185969, A248907, A256179.

Sequence in context: A175399 * A133500 A256229 A052423 A126616 A121042

Adjacent sequences:  A075874 A075875 A075876 * A075878 A075879 A075880

KEYWORD

nonn,base,hear,look

AUTHOR

Reinhard Zumkeller, Oct 16 2002

EXTENSIONS

Formula corrected by Reinhard Zumkeller, May 27 2013

Edited by M. F. Hasler, Mar 22 2015

STATUS

approved

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Last modified June 27 15:10 EDT 2017. Contains 288790 sequences.