A367697 -id:A367697 - cp's OEIS frontend

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

Amiram Eldar, Nov 27 2023

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... .

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

Subsequence of A270428.
Subsequences: A007674, A367697.
Similar sequences: A071318, A121495, A340152, A367695.

expOdQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ[DigitCount[#, 2, 1]] &]; Select[Range[100], And @@ expOdQ /@ {#, # + 1} &]

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)

cp's OEIS Frontend

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

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