A339239 Binary self numbers (A010061) with a record gap to the next binary self number.

1, 6, 63, 250, 131070, 1048574, 33554426, 17179869180

Offset: 1

Author

Amiram Eldar, Nov 28 2020

Keywords

• nonn
• base
• more

Comments

The corresponding gaps are 3, 7, 8, 20, 21, 24, 37, 42, ...

a(9) <= 288230376151711738.

Apparently, the records gaps occur for pairs of consecutive binary self numbers with a power of 2 between them. If this is generally true, then the next terms are 288230376151711738, 147573952589676412923, 37778931862957161709564, 10633823966279326983230456482242756602, 5444517870735015415413993718908291383294, 43556142965880123323311949751266331066367, ..., with the corresponding gaps 70, 77, 83, 135, 136, 137, ...

Examples

			The first 4 binary self numbers are 1, 4, 6 and 13. The gaps between them are 3, 2 and 7. The record gaps are 3 and 7, and the corresponding terms are 1 and 6.
		

Crossrefs

Cf. A010061, A339216.

Programs

Mathematica

s[n_] := n + DigitCount[n, 2, 1]; selfQ[n_] := AllTrue[Range[n, n - Floor@Log2[n], -1], s[#] != n &]; dm = 0; seq = {}; n1 = 1; Do[If[selfQ[n], d = n - n1; If[d > dm, dm = d; AppendTo[seq, n1]]; n1 = n], {n, 2, 150000}]; seq