A010345 Base-5 Armstrong or narcissistic numbers, written in base 5.

1, 2, 3, 4, 23, 33, 103, 433, 2124, 2403, 3134, 124030, 124031, 242423, 434434444, 1143204434402, 14421440424444

Offset: 1

Author

N. J. A. Sloane

Keywords

• base
• fini
• full
• nonn

Comments

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

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

Links

• Gordon L. Miller and Mary T. Whalen, Armstrong Numbers: 153 = 1^3 + 5^3 + 3^3, Fibonacci Quarterly, 30-3 (1992), 221-224. See Table 4 p. 223.
• Eric Weisstein's World of Mathematics, Narcissistic Number
• D. T. Winter, Table of Armstrong Numbers (latest backup on web.archive.org from Jan. 2010; page no longer available), published not later than Aug. 2003.

Crossrefs

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

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

Programs

PARI

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

Extensions

Edited by Joseph Myers, Jun 28 2009