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

1,1

Comments

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

Links

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.

Example

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.

Mathematica

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

Crossrefs

Cf. A006753, A019506, A050219, A235766.

Sequence in context: A251254 A349682 A064198 * A233055 A233056 A211260

Adjacent sequences: A329932 A329933 A329934 * A329936 A329937 A329938

Keyword

nonn,base

Author

Amiram Eldar, Nov 24 2019

Status

approved