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A101337
Sum of (each digit of n raised to the power (number of digits in n)).
21
1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 4, 5, 8, 13, 20, 29, 40, 53, 68, 85, 9, 10, 13, 18, 25, 34, 45, 58, 73, 90, 16, 17, 20, 25, 32, 41, 52, 65, 80, 97, 25, 26, 29, 34, 41, 50, 61, 74, 89, 106, 36, 37, 40, 45, 52, 61, 72, 85, 100, 117, 49, 50, 53, 58, 65
OFFSET
1,2
COMMENTS
Sometimes referred to as "narcissistic function" (in base 10). Fixed points are the narcissistic (or Armstrong, or plus perfect) numbers A005188. - M. F. Hasler, Nov 17 2019
LINKS
Wikipedia, Narcissistic number, as of Nov 18 2019.
FORMULA
a(n) <= A055642(n)*9^A055642(n) with equality for all n = 10^k - 1. Write n = 10^x to get a(n) < n when 1+log_10(x+1) < (x+1)(1-log_10(9)) <=> x > 59.85. It appears that a(n) < n already for all n > 1.02*10^59. - M. F. Hasler, Nov 17 2019
EXAMPLE
a(75) = 7^2 + 5^2 = 74 and a(705) = 7^3 + 0^3 + 5^3 = 468.
a(1.02e59 - 1) = 102429587095122578993551250282047487264694110769657513064859 ~ 1.024e59 is an example of n close to the limit beyond which a(n) < n for all n. - M. F. Hasler, Nov 17 2019
MATHEMATICA
Array[Total[IntegerDigits[#]^IntegerLength[#]]&, 80] (* Harvey P. Dale, Aug 27 2011 *)
PROG
(PARI) a(n)=my(d=digits(n)); sum(i=1, #d, d[i]^#d) \\ Charles R Greathouse IV, Aug 10 2017
(PARI) apply( A101337(n)=vecsum([d^#n|d<-n=digits(n)]), [0..99]) \\ M. F. Hasler, Nov 17 2019
(Python)
def A101337(n):
s = str(n)
l = len(s)
return sum(int(d)**l for d in s) # Chai Wah Wu, Feb 26 2019
(Magma) f:=func<n|&+[Intseq(n)[i]^#Intseq(n):i in [1..#Intseq(n)]]>; [f(n):n in [1..75]]; // Marius A. Burtea, Nov 18 2019
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Gordon Hamilton, Dec 24 2004
EXTENSIONS
Name changed by Axel Harvey, Dec 26 2011
Edited by M. F. Hasler, Nov 17 2019
STATUS
approved