

A073799


Numbers that begin a run of consecutive integers k such that PrimePi(k) divides 2^k.


2



2, 7, 19, 53, 131, 311, 719, 1619, 3671, 8161, 17863, 38873, 84017, 180503, 386093, 821641, 1742537, 3681131
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OFFSET

1,1


COMMENTS

It seems that each term is a bit larger than twice the previous one.
Runs have lengths 3, 4, 4, 6, 6, 2, 8, 2, 2, 6, 18, 18, 30, 8, 24, 6, 2, 18, ..., respectively.


LINKS

Table of n, a(n) for n=1..18.


FORMULA

Solutions to 2^(x1) mod PrimePi(x1) > 0 but 2^x mod PrimePi(x) = 0.


MATHEMATICA

aQ[k_] := Divisible[2^k, PrimePi[k]]; s = {}; len = {}; n = 2; While[Length[s] < 10, While[! aQ[n], n++]; n1 = n; While[aQ[n], n++]; If[n > n1, AppendTo[s, n1]; AppendTo[len, n  n1]]; n++]; s (* Amiram Eldar, Dec 11 2018 *)


CROSSREFS

Cf. A000079, A000720, A015910, A062173, A064367, A073797, A073798.
Cf. A033844.  R. J. Mathar, Sep 23 2008
Sequence in context: A099484 A018030 A051354 * A040016 A145519 A030224
Adjacent sequences: A073796 A073797 A073798 * A073800 A073801 A073802


KEYWORD

nonn,more


AUTHOR

Labos Elemer, Aug 12 2002


EXTENSIONS

Edited by Jon E. Schoenfield, Dec 10 2018
a(15)a(18) from Amiram Eldar, Dec 11 2018


STATUS

approved



