

A138104


2^(nth semiprime)  1.


0



15, 63, 511, 1023, 16383, 32767, 2097151, 4194303, 33554431, 67108863, 8589934591, 17179869183, 34359738367, 274877906943, 549755813887, 70368744177663, 562949953421311, 2251799813685247, 36028797018963967
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OFFSET

1,1


COMMENTS

This is a semiprime analog of A001348 Mersenne numbers. The semiprimes in this sequence are the analogs of A000668 Mersenne primes (of form 2^p  1 where p is a prime). a(n) is semiprime when a(n) is an element of A092561, which happens for values of n beginning 1, 3, 17, which is A085724 INTERSECTION A001358 and has no more values under 1000. Would someone like to extend the latter set of indices j of semiprimes k = A001358(j) such that (2^k)1 is semiprime?


LINKS

Table of n, a(n) for n=1..19.


FORMULA

a(n) = (2^A001358(n))1.


EXAMPLE

a(1) = (2^4)  1 = 15 because 4 is the 1st semiprime. Note that 15 = 3*5 is itself semiprime.
a(2) = (2^6)  1 = 63 because 6 is the 2nd semiprime. Note that 63 = (3^2)*7 is not itself semiprime.
a(3) = (2^9)  1 = 511 because 9 is the 3rd semiprime; and 511 = 7 * 73 is itself semiprime.
a(17) = (2^17)1 = 562949953421311 = 127 * 4432676798593, itself semiprime.


MATHEMATICA

2^#1&/@Select[Range[100], PrimeOmega[#]==2&] (* Harvey P. Dale, Jun 26 2011 *)


CROSSREFS

Cf. A000668, A001348, A001358, A085724, A092561.
Sequence in context: A305616 A104473 A135972 * A152099 A119496 A044153
Adjacent sequences: A138101 A138102 A138103 * A138105 A138106 A138107


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, May 03 2008


STATUS

approved



