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A325058 Starts of runs of 7 consecutive exponentially odd numbers (A268335). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A134100 A060769 A031925 * A107134 A139851 A139895

Adjacent sequences:  A325055 A325056 A325057 * A325059 A325060 A325061

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 04 2019

STATUS

approved

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Last modified October 17 11:43 EDT 2021. Contains 348048 sequences. (Running on oeis4.)