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A339239
Binary self numbers (A010061) with a record gap to the next binary self number.
0
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, ...
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
Sequence in context: A222079 A158987 A374227 * A055005 A027811 A027950
KEYWORD
nonn,base,more
AUTHOR
Amiram Eldar, Nov 28 2020
STATUS
approved