A010345 - OEIS

%I #42 Feb 16 2025 08:32:32

%S 1,2,3,4,23,33,103,433,2124,2403,3134,124030,124031,242423,434434444,

%T 1143204434402,14421440424444

%N Base-5 Armstrong or narcissistic numbers, written in base 5.

%C Also called Perfect Digital Invariant (PDI). When a(n) ends in 0, then a(n+1) = a(n) + 1 is also in the sequence, but in this base this only happens once. Zero would also satisfy the definition (n = Sum_{i=1..k} d[i]^k where d[1..k] are the base-5 digits of n), like the other single-digit terms. - _M. F. Hasler_, Nov 18 2019

%C The property of being an Armstrong number is an arithmetic property (like the number of divisors function) and is usually restricted to positive numbers. - _N. J. A. Sloane_, Nov 29 2019

%H Gordon L. Miller and Mary T. Whalen, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/30-3/miller.pdf">Armstrong Numbers: 153 = 1^3 + 5^3 + 3^3</a>, Fibonacci Quarterly, 30-3 (1992), 221-224. See Table 4 p. 223.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number</a>

%H D. T. Winter, <a href="http://web.archive.org/web/20100109234250/http://ftp.cwi.nl:80/dik/Armstrong">Table of Armstrong Numbers</a> (latest backup on web.archive.org from Jan. 2010; page no longer available), published not later than Aug. 2003.

%o (PARI) A010345=[fromdigits(digits(n,5))|n<-A010346] \\ Assumes the vector A010346 defined, see there for code. - _M. F. Hasler_, Nov 18 2019

%Y Cf. A010346 (a(n) written in base 10).

%Y In other bases: A010343 (base 4), A010347 (base 6), A010349 (base 7), A010351 (base 8), A010352 (base 9), A005188 (base 10).

%K base,fini,full,nonn,changed

%O 1,2

%A _N. J. A. Sloane_

%E Edited by _Joseph Myers_, Jun 28 2009