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A339213
Phi-base self numbers: positive numbers not of the form k + A055778(k).
8
1, 3, 6, 10, 12, 15, 19, 23, 26, 30, 32, 38, 41, 43, 52, 55, 59, 61, 64, 68, 72, 75, 79, 81, 86, 89, 91, 97, 101, 104, 108, 110, 115, 118, 120, 126, 131, 135, 137, 140, 144, 148, 151, 155, 157, 163, 166, 168, 177, 180, 184, 186, 189, 193, 197, 200, 204, 206, 213
OFFSET
1,2
COMMENTS
Analogous to self numbers (A003052) using base phi (A130600) instead of base 10.
REFERENCES
József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.
MATHEMATICA
s[1] = 2; s[n_] := n + Plus @@ RealDigits[n, GoldenRatio, 2*Ceiling[Log[GoldenRatio, n]]][[1]]; m = 220; Complement[Range[m], Array[s, m]]
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Nov 27 2020
STATUS
approved