OFFSET
1,1
COMMENTS
The maximal run of consecutive exponentially odd numbers is of length 7 since numbers of the form 8k + 4 are not exponentially odd. Thus all the terms of this sequence are of the form 8k + 5 with k = 3, 4, 6, 12, 16, 22, 26, 46, 56, 63, 67, 76, 84, 94, ...
The number of terms below 10^k for k = 2, 3, ... is 3, 18, 201, 1878, 18902, 189515, 1895392, 18954089, ... Apparently this sequence has an asymptotic density of 0.01895...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
29 is in the sequence since 29, 30 = 2 * 3 * 5, 31, 32 = 2^5, 33 = 3 * 11, 34 = 2 * 17 and 35 = 5 * 7 are 7 consecutive exponentially odd numbers, all having prime factorization with only odd exponents.
MATHEMATICA
expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; aQ[n_] := AllTrue[8n + Range[5, 11], expOddQ]; 8 * Select[Range[300], aQ] + 5
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 04 2019
STATUS
approved