A385487 Records in A385485.

3, 7, 29, 65, 69, 81, 257, 259, 4097, 4113, 4129, 262145, 262149, 1048577, 1048583, 16777217, 16777219, 38347927, 214748365, 214748369, 4294967297, 4294967299, 68719476737, 68719476769, 1099511627777, 4398046511105, 4398046511109

Offset: 1

Author

Amiram Eldar, Jun 30 2025

Keywords

• nonn
• base
• more

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..27

Crossrefs

Cf. A049445, A144375 (decimal analog), A385484, A385485, A385486 (indices of records).

Programs

Mathematica

f[n_] := Module[{m = n, k = 1}, While[Divisible[m, DigitSum[m, 2]], m += 2*n; k += 2]; k];
seq[lim_] := Module[{s = {}, fm = -1, fi}, Do[fi = f[i]; If[fi > fm, fm = fi; AppendTo[s, fi]], {i, 1, lim}]; s]; seq[10^4]

PARI

f(n) = {my(m = n, k = 1); while(!(m % hammingweight(m)), m += 2*n; k += 2); k;}
list(lim) = my(fm = -1, fi); for(i = 1, lim, fi = f(i); if(fi > fm, fm = fi; print1(fi, ", ")));

Formula

a(n) = A385485(A385486(n)).

Extensions

a(21)-a(27) from Chai Wah Wu, Jul 02 2025