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A138104 2^(n-th semiprime) - 1. 0
15, 63, 511, 1023, 16383, 32767, 2097151, 4194303, 33554431, 67108863, 8589934591, 17179869183, 34359738367, 274877906943, 549755813887, 70368744177663, 562949953421311, 2251799813685247, 36028797018963967 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 16:10 EST 2018. Contains 317323 sequences. (Running on oeis4.)