

A115392


First appearance of nth prime as prime factor in list of semiprimes.


3



1, 2, 4, 5, 8, 10, 12, 14, 16, 21, 22, 25, 27, 29, 33, 35, 38, 41, 45, 47, 50, 52, 55, 58, 62, 64, 67, 70, 73, 76, 82, 84, 87, 88, 93, 96, 100, 104, 107, 111, 113, 115, 120, 121, 124, 126, 133, 137, 141, 142, 143, 147, 149, 155, 158, 162, 168, 169, 174, 176, 178, 183
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OFFSET

1,2


COMMENTS

The positions of even semiprimes in A001358.  JuriStepan Gerasimov, Apr 11 2010


LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000


FORMULA

A001358(a(n)) = 2*A000040(n)  Zak Seidov, Jun 27 2017


EXAMPLE

a(5)=8 because 5th prime, 11, first appeared as a prime factor in 8th semiprime 22=2*11;
a(6)=10 because 6th prime, 13, first appeared as a prime factor in 10th semiprime 26=2*13.


MATHEMATICA

sp = Select[Range[4, 20000], 2 == PrimeOmega[#]&]; Table[Position[Mod[sp, Prime[k]], 0][[1, 1]], {k, 1000}] (* For first 1000 terms.  Zak Seidov, Jun 27 2017 *)


PROG

(PARI) first(n) = my(l = List([4, 1]), u = 2*prime(n), res = vector(n), t=0); forprime(p = 2, t++; sqrt(2*prime(n)), forprime(q = p+1, u\p, listput(l, [p*q, t])); listsort(l); for(i=1, #l, if(res[l[i][3]]==0, res[l[i][3]] = i)) \\ David A. Corneth, Jun 28 2017


CROSSREFS

Cf. A000040, A001358.
Sequence in context: A005242 A323976 A188975 * A179509 A157007 A173509
Adjacent sequences: A115389 A115390 A115391 * A115393 A115394 A115395


KEYWORD

nonn


AUTHOR

Zak Seidov, Mar 08 2006


EXTENSIONS

Edited by Zak Seidov, Jun 27 2017


STATUS

approved



