This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344513 #7 Feb 16 2025 08:34:02
%S A344513 4,13,287,294,6564,90163,1136828,3301262,276404649,5643189146
%N A344513 a(n) is the least number larger than 1 which is a self number in all the even bases b = 2*k for 1 <= k <= n.
%C A344513 Joshi (1973) proved that for all odd b the sequence of base-b self numbers is the sequence of odd numbers (A005408). Therefore, in this sequence the bases are restricted to even values. For the corresponding sequence with both odd and even bases, see A344512.
%D A344513 Vijayshankar Shivshankar Joshi, Contributions to the theory of power-free integers and self-numbers, Ph.D. dissertation, Gujarat University, Ahmedabad (India), October, 1973.
%D A344513 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.
%H A344513 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SelfNumber.html">Self Number</a>.
%H A344513 Wikipedia, <a href="http://en.wikipedia.org/wiki/Self_number">Self number</a>.
%H A344513 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e A344513 a(1) = 4 since the least binary self number after 1 is A010061(2) = 4.
%e A344513 a(2) = 13 since the least binary self number after 1 which is also a self number in base 2*2 = 4 is A010061(4) = A010064(4) = 13.
%t A344513 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[1] = 4; a[n_] := a[n] = Module[{k = a[n - 1]}, While[! AllTrue[Range[1, n], selfQ[k, 2*#] &], k++]; k]; Array[a, 7]
%Y A344513 Cf. A003052, A010061, A010064, A010067, A010070, A339211, A339212, A339213, A339214, A339215, A342729, A344512.
%Y A344513 Similar sequences: A016038, A217705, A225427, A226320, A228768, A258107.
%K A344513 nonn,base,more
%O A344513 1,1
%A A344513 _Amiram Eldar_, May 21 2021