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Factorial-base self numbers: numbers not of the form k + A034968(k).
8

%I #15 Feb 16 2025 08:34:01

%S 1,4,11,18,36,43,61,68,86,93,111,118,125,132,139,157,164,182,189,207,

%T 214,232,239,246,253,260,278,285,303,310,328,335,353,360,367,374,381,

%U 399,406,424,431,449,456,474,481,488,495,502,520

%N Factorial-base self numbers: numbers not of the form k + A034968(k).

%C Analogous to self numbers (A003052) using factorial base representation (A007623) instead of decimal expansion.

%D József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.

%H Amiram Eldar, <a href="/A339214/b339214.txt">Table of n, a(n) for n = 1..10000</a>

%H Rosalind Guaraldo, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/16-6/guaraldo.pdf">On the Density of the Image Sets of Certain Arithmetic Functions - III</a>, The Fibonacci Quarterly, Vol. 16, No. 6 (1978), pp. 481-488.

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system">Factorial number system</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Self_number">Self number</a>.

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%t max = 6; s[n_] := n + Plus @@ IntegerDigits[n, MixedRadix[Range[max, 2, -1]]]; m = max!; Complement[Range[m], Array[s, m]]

%Y Cf. A003052, A007623, A010061, A010064, A010067, A010070, A034968, A118363, A339211, A339212, A339213, A339215.

%Y Cf. also A219650, A219658, A230412.

%K nonn,base,changed

%O 1,2

%A _Amiram Eldar_, Nov 27 2020