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

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

Offset

1,2

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, ...

Links

Table of n, a(n) for n=1..8.

Example

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.

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

Crossrefs

Cf. A010061, A339216.

Sequence in context: A222079 A158987 A374227 * A055005 A027811 A027950

Adjacent sequences: A339236 A339237 A339238 * A339240 A339241 A339242

Keyword

nonn,base,more

Author

Amiram Eldar, Nov 28 2020

Status

approved