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Base-7 Armstrong or narcissistic numbers, written in base 7.
8

%I #33 Jan 17 2020 14:06:54

%S 1,2,3,4,5,6,13,34,44,63,250,251,305,505,12205,12252,13350,13351,

%T 15124,36034,205145,1424553,1433554,3126542,4355653,6515652,125543055,

%U 161340144,254603255,336133614,542662326,565264226,13210652042,13213641035,13261421245,23662020022,52112660266

%N Base-7 Armstrong or narcissistic numbers, written in base 7.

%C From _M. F. Hasler_, Nov 20 2019: (Start)

%C 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 7 digits of n), but here only positive numbers are considered.

%C Whenever a(n) ends in zero (n = 11, 17, 22, 38, 57), then a(n+1) = a(n) + 1 is also a solution to the above equation. (End)

%H Joseph Myers, <a href="/A010349/b010349.txt">Table of n, a(n) for n = 1..59</a> (the full list of terms, from Winter)

%H Gordon L. Miller and Mary T. Whalen, <a href="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.

%H Eric Weisstein's World of Mathematics, <a href="http://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) [fromdigits(digits(n,7))|n<-A010350] \\ _M. F. Hasler_, Nov 18 2019

%Y Cf. A010350 (a(n) written in base 10).

%Y In other bases: A010343 (base 4), A010345 (base 5), A010347 (base 6), A010351 (base 8), A010352 (base 9), A005188 (base 10).

%K base,fini,full,nonn

%O 1,2

%A _N. J. A. Sloane_

%E Edited by _Joseph Myers_, Jun 28 2009