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 A344512 a(n) is the least number larger than 1 which is a self number in all the bases 2 <= b <= n. 1
 4, 13, 13, 13, 287, 287, 2971, 2971, 27163, 27163, 90163, 90163, 5940609, 5940609, 6069129, 6069129, 276404649, 276404649 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Since the sequence of base-b self numbers for odd b is the sequence of the odd numbers (A005408) (Joshi, 1973), all the terms beyond a(2) are odd numbers. For the corresponding sequence with only even bases, see A344513. a(20) > 1.5*10^10, if it exists. REFERENCES Vijayshankar Shivshankar Joshi, Contributions to the theory of power-free integers and self-numbers, Ph.D. dissertation, Gujarat University, Ahmedabad (India), October, 1973. József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386. LINKS Table of n, a(n) for n=2..19. Eric Weisstein's World of Mathematics, Self Number. Wikipedia, Self number. Index entries for Colombian or self numbers and related sequences FORMULA a(2*n+1) = a(2*n) for n >= 2. EXAMPLE a(2) = 4 since the least binary self number after 1 is A010061(2) = 4. a(3) = 13 since the least binary self number after 1 which is also a self number in base 3 is A010061(4) = 13. MATHEMATICA s[n_, b_] := n + Plus @@ IntegerDigits[n, b]; selfQ[n_, b_] := AllTrue[Range[n, n - (b - 1) * Ceiling @ Log[b, n], -1], s[#, b] != n &]; a[2] = 4; a[b_] := a[b] = Module[{n = a[b - 1]}, While[! AllTrue[Range[2, b], selfQ[n, #] &], n++]; n]; Array[a, 10, 2] CROSSREFS Cf. A003052, A010061, A010064, A010067, A010070, A339211, A339212, A339213, A339214, A339215, A342729, A344513. Similar sequences: A016038, A217705, A225427, A226320, A228768, A258107. Sequence in context: A287895 A050223 A301792 * A168401 A370644 A081738 Adjacent sequences: A344509 A344510 A344511 * A344513 A344514 A344515 KEYWORD nonn,base,more AUTHOR Amiram Eldar, May 21 2021 STATUS approved

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Last modified September 12 15:03 EDT 2024. Contains 375852 sequences. (Running on oeis4.)