

A101337


Sum of (each digit of n raised to the power (number of digits in n)).


16



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
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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

Michael De Vlieger, Table of n, a(n) for n = 1..10000
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)(1log_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^#nd<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

Cf. A179239, A306360.
Sequence in context: A247796 A326344 A115026 * A135208 A259043 A156207
Adjacent sequences: A101334 A101335 A101336 * A101338 A101339 A101340


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



