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

1,2

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

Table of n, a(n) for n=1..17.

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.

Prog

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

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).

Sequence in context: A115884 A331603 A171728 * A233344 A329566 A329532

Adjacent sequences: A010342 A010343 A010344 * A010346 A010347 A010348

Keyword

base,fini,full,nonn

Author

N. J. A. Sloane

Extensions

Edited by Joseph Myers, Jun 28 2009

Status

approved