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A367696
Numbers k such that k and k+1 are both exponentially odious numbers (A270428).
3
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 28, 29, 30, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85
OFFSET
1,2
COMMENTS
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 8, 78, 762, 7615, 76113, 761127, 7611222, 76111895, 761119135, 7611190807, ... . Apparently, the asymptotic density of this sequence exists and equals 0.761119... .
LINKS
MATHEMATICA
expOdQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ[DigitCount[#, 2, 1]] &]; Select[Range[100], And @@ expOdQ /@ {#, # + 1} &]
PROG
(PARI) isexpod(n) = {my(f = factor(n)); for(i=1, #f~, if (!(hammingweight(f[i, 2]) % 2), return (0))); 1; }
is(n) = isexpod(n) && isexpod(n+1)
CROSSREFS
Subsequence of A270428.
Subsequences: A007674, A367697.
Similar sequences: A071318, A121495, A340152, A367695.
Sequence in context: A245606 A269864 A103681 * A319824 A039265 A073599
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Nov 27 2023
STATUS
approved