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A329935
Numbers k such that k and k+1 are both hoax numbers (A019506).
2
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
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Nov 24 2019
STATUS
approved