

A115392


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


26



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 * A342541 A179509 A157007
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



