A115392 First appearance of n-th prime as prime factor in list of semiprimes.

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

Offset

1,2

Comments

The positions of even semiprimes in A001358. - Juri-Stepan 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 A365315 A179509

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