A325058 Starts of runs of 7 consecutive exponentially odd numbers (A268335).

29, 37, 53, 101, 133, 181, 213, 373, 453, 509, 541, 613, 677, 757, 893, 901, 917, 997, 1109, 1117, 1157, 1189, 1237, 1253, 1333, 1405, 1429, 1477, 1509, 1541, 1589, 1621, 1701, 1749, 1757, 1765, 1829, 1885, 1941, 2077, 2117, 2133, 2181, 2213, 2261, 2333, 2341

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

Cf. A268335.

Sequence in context: A060769 A355161 A031925 * A107134 A139851 A139895

Adjacent sequences: A325055 A325056 A325057 * A325059 A325060 A325061

Keyword

nonn

Author

Amiram Eldar, Sep 04 2019

Status

approved