A010347 Base-6 Armstrong or narcissistic numbers, written in base 6.

1, 2, 3, 4, 5, 243, 514, 14340, 14341, 14432, 23520, 23521, 44405, 435152, 5435254, 12222215, 555435035, 1053025020422, 1053122514003, 1435403205450, 1435403205451, 1450005114454, 2135254510352, 2145555022413, 2500150125455, 133024510545125

Offset: 1

Author

N. J. A. Sloane

Keywords

• base
• fini
• full
• nonn

Comments

From M. F. Hasler, Nov 18 2019: (Start)

Whenever a(n) ends in 0 (n = 8, 11, 20, 28), then a(n+1) = a(n) + 1 also satisfies the definition.

Like the other single-digit terms, zero would satisfy the definition (n = Sum_{i=1..k} d[i]^k where d[1..k] are the base 6 digits of n), but here only positive numbers are considered. (End)

Links

• Joseph Myers, Table of n, a(n) for n = 1..30 (the full list of terms, from Winter)
• Gordon L. Miller and Mary T. Whalen, Armstrong Numbers: 153 = 1^3 + 5^3 + 3^3, Fibonacci Quarterly, 30-3 (1992), 221-224.
• 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. A010348 (a(n) written in base 10).

In other bases: A010343 (base 4), A010345 (base 5), A010349 (base 7), A010351 (base 8), A010352 (base 9), A005188 (base 10).

Programs

PARI

A010347=[fromdigits(digits(n,6))|n<-A010348] \\ M. F. Hasler, Nov 18 2019

PARI

select( is_A010347(n)={vecmax(n=digits(n+!n))<6 && vecsum([d^#n|d<-n])==fromdigits(n,6)}, [0..10^5]) \\ M. F. Hasler, Nov 20 2019

Extensions

Edited by Joseph Myers, Jun 28 2009