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a(n) begins the first run of exactly n consecutive binary hoax numbers (A329936).
1

%I #16 Nov 29 2019 01:38:58

%S 4,8,49,3952,117175,2322232,2437094,15449349,438134200,1605609902,

%T 85678432036,132891678661,8415592788756

%N a(n) begins the first run of exactly n consecutive binary hoax numbers (A329936).

%C a(14) > 10^13, a(15) = 6359937801959. - _Giovanni Resta_, Nov 28 2019

%e a(2) = 8 since 8 and 9 are binary hoax numbers.

%e a(3) = 49 since 49, 50, and 51 are binary hoax numbers.

%t binWt[n_] := Total@IntegerDigits[n, 2]; binHoaxQ[n_] := CompositeQ[n] && Total[binWt /@ FactorInteger[n][[;; , 1]]] == binWt[n]; n = 1; count = 0; max = 6; seq = Table[0, {max}]; While[count < max, n1 = n; If[binHoaxQ[n], While[binHoaxQ[++n1]]; d = n1 - n; If[d <= max && seq[[d]] == 0, count++; seq[[d]] = n]]; n = n1 + 1]; seq

%Y Cf. A019506, A235766, A329936.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Nov 24 2019

%E a(11)-a(13) from _Giovanni Resta_, Nov 28 2019