A344513 -id:A344513 - cp's OEIS frontend

A344512 a(n) is the least number larger than 1 which is a self number in all the bases 2 <= b <= n.

4, 13, 13, 13, 287, 287, 2971, 2971, 27163, 27163, 90163, 90163, 5940609, 5940609, 6069129, 6069129, 276404649, 276404649

Offset: 2

Amiram Eldar, May 21 2021

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.

			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.

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.

Eric Weisstein's World of Mathematics, Self Number.
Wikipedia, Self number.
Index entries for Colombian or self numbers and related sequences

Cf. A003052, A010061, A010064, A010067, A010070, A339211, A339212, A339213, A339214, A339215, A342729, A344513.

Similar sequences: A016038, A217705, A225427, A226320, A228768, A258107.

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]

a(2*n+1) = a(2*n) for n >= 2.

cp's OEIS Frontend

A344512 a(n) is the least number larger than 1 which is a self number in all the bases 2 <= b <= n.

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