

A109926


Least k such that k2^r is prime for n values of r. Index of the first occurrence of n in A109925.


1



1, 3, 4, 15, 21, 45, 75, 465, 1095, 2145, 4935, 14955, 80685, 229845, 1295325, 1575285, 9700575, 20435415, 15054105, 53999715, 2282745465
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OFFSET

0,2


COMMENTS

It appears that 3 and 5 divide a(n) for n>4. Note that a(18)<a(17).  T. D. Noe, Jul 19 2005
Conjecture: a(n)==0 (mod 3) for n > 2. Then n2^k is not == 0 (mod 3) and a prime is more probable.  Robert G. Wilson v, Jul 21 2005
Conjecture: a(n+15)==0 (mod 30) for n > 4.  Robert G. Wilson v, Jul 21 2005
a(n) > 10^10 for n >= 21.  Donovan Johnson, Jan 21 2009


LINKS

Table of n, a(n) for n=0..20.


EXAMPLE

a(4) = 21, 212 =19, 214 = 17, 218 = 13, 2116 = 5, 21 is the smallest number that gives four such primes.


MATHEMATICA

t=Table[cnt=0; r=1; While[r<n, If[PrimeQ[nr], cnt++ ]; r=2r]; cnt, {n, 250000}]; Table[First[Flatten[Position[t, n]]], {n, 13}] (Noe)
f[n_] := Count[ PrimeQ[n  2^Range[0, Floor[ Log[2, n]]]], True]; t = Table[0, {30}]; Do[ a = f[n]; If[ t[[a+1]] == 0, t[[a+1]] = n], {n, 4*10^8}]; t (* Robert G. Wilson v *)


CROSSREFS

Cf. A109925.
Sequence in context: A136210 A041819 A095799 * A272514 A065942 A036759
Adjacent sequences: A109923 A109924 A109925 * A109927 A109928 A109929


KEYWORD

hard,more,nonn


AUTHOR

Amarnath Murthy, Jul 17 2005


EXTENSIONS

Edited, corrected and extended by T. D. Noe and Robert G. Wilson v, Jul 19 2005
a(20) from Donovan Johnson, Jan 21 2009


STATUS

approved



