A235766 -id:A235766 - cp's OEIS frontend

A329935 Numbers k such that k and k+1 are both hoax numbers (A019506).

84, 516, 644, 860, 2325, 3344, 4188, 4980, 5268, 5484, 6259, 6603, 6692, 6980, 7051, 7195, 8076, 8420, 9716, 10704, 11774, 12795, 12955, 12956, 13747, 14475, 14715, 14724, 16473, 17148, 17149, 17225, 17661, 19175, 21828, 22143, 22347, 24259, 24272, 24980

Offset: 1

Amiram Eldar, Nov 24 2019

Analogous to A050219 (smaller of Smith brothers) as A019506 (hoax numbers) is analogous to A006753 (Smith numbers).

			84 is in the sequence since 84 is a hoax number: 84 = 2^2 * 3 * 7 and 8 + 4 = 2 + 3 + 7 = 12, and 85 = 84 + 1 is also a hoax number: 85 = 5 * 17 and 8 + 5 = 5 + 1 + 7 = 13.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, page 27, entry 85.

Cf. A006753, A019506, A050219, A235766.

digitSum[n_]  := Total @ IntegerDigits[n]; hoaxQ[n_] := CompositeQ[n] && Total[ digitSum /@ FactorInteger[n][[;; , 1]] ] == digitSum[n]; seq = {}; isHoax1 = hoaxQ[1]; Do[isHoax2 = hoaxQ[n]; If[isHoax1 && isHoax2, AppendTo[seq, n-1]]; isHoax1 = isHoax2, {n, 2, 25000}]; seq

A329942 a(n) begins the first run of exactly n consecutive binary hoax numbers (A329936).

Original entry on oeis.org

4, 8, 49, 3952, 117175, 2322232, 2437094, 15449349, 438134200, 1605609902, 85678432036, 132891678661, 8415592788756

Offset: 1

Amiram Eldar, Nov 24 2019

a(14) > 10^13, a(15) = 6359937801959. - Giovanni Resta, Nov 28 2019

			a(2) = 8 since 8 and 9 are binary hoax numbers.
a(3) = 49 since 49, 50, and 51 are binary hoax numbers.

Cf. A019506, A235766, A329936.

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

a(11)-a(13) from Giovanni Resta, Nov 28 2019

cp's OEIS Frontend

A329935 Numbers k such that k and k+1 are both hoax numbers (A019506).

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