A329935 - OEIS

%I #18 Aug 22 2020 18:49:30

%S 84,516,644,860,2325,3344,4188,4980,5268,5484,6259,6603,6692,6980,

%T 7051,7195,8076,8420,9716,10704,11774,12795,12955,12956,13747,14475,

%U 14715,14724,16473,17148,17149,17225,17661,19175,21828,22143,22347,24259,24272,24980

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

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

%H Amiram Eldar, <a href="/A329935/b329935.txt">Table of n, a(n) for n = 1..10000</a>

%H Jean-Marie De Koninck, <a href="https://bookstore.ams.org/mbk-64/47">Those Fascinating Numbers</a>, American Mathematical Society, 2009, page 27, entry 85.

%e 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.

%t 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

%Y Cf. A006753, A019506, A050219, A235766.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Nov 24 2019