A367696 Numbers k such that k and k+1 are both exponentially odious numbers (A270428).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A367693 A367694 A367695 * A367697 A367698 A367699

Keyword

nonn,base

Author

Amiram Eldar, Nov 27 2023

Status

approved