This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A251724 a(1) = 2, and for n>1: a(n) = prime(A251719(n)) * prime(A251719(n) + n - 2), where prime(n) gives the n-th prime. 5
 2, 4, 6, 21, 65, 85, 95, 115, 217, 259, 287, 301, 329, 649, 671, 737, 781, 803, 869, 913, 979, 1067, 1111, 1133, 1177, 1199, 1243, 1703, 1781, 1807, 1937, 1963, 2041, 2119, 2171, 3043, 3077, 3247, 3281, 3349, 3383, 3587, 3791, 3859, 3893, 3961, 4063, 4097, 4267, 4369, 4471, 4573, 4607, 4709, 4777, 4811, 5833, 5909, 5947, 6023, 6289, 6403, 6593, 6631, 6707, 6821, 8579 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For n >= 2: a(n) = the first "settled semiprime" in the column n of the sieve of Eratosthenes: a(n) = A083221(A251719(n), n). The "settling of semiprimes" here means that from that semiprime onward, all the other terms in the same column n of a square array A083221 (which is constructed from the sieve of Eratosthenes) are also semiprimes, obtained by successive iterations of A003961 starting from the semiprime here given as a(n). Cf. comments in A251728 which contains all such semiprimes. The "unsettled" semiprimes are in its complement A138511. Here we assume that A054272(n), the number of primes in interval [p(n), p(n)^2], is nondecreasing (implied for example if Legendre's or Brocard's conjecture is true). LINKS Antti Karttunen, Table of n, a(n) for n = 1..10351 Wikipedia, Brocard's Conjecture FORMULA a(1) = 2; and for n >= 2: a(n) = A000040(A251719(n)) * A000040(A251719(n) + n - 2). a(n) = A083221(A251719(n), n). Other identities implied by the definition. For all n >= 1: A078898(a(n)) = n. A055396(a(n)) = A251719(n). For all n >= 2: A243055(a(n)) = n-2. PROG (Scheme, two versions) (define (A251724 n) (if (= 1 n) 2 (* (A000040 (A251719 n)) (A000040 (+ (A251719 n) n -2))))) (define (A251724 n) (A083221bi (A251719 n) n)) CROSSREFS After initial 2, a subsequence of A251728 and A001358. Cf. A000040, A003961, A054272, A055396, A078898, A083221, A138511, A243055, A251719. Sequence in context: A193774 A241210 A176652 * A326363 A273522 A227626 Adjacent sequences:  A251721 A251722 A251723 * A251725 A251726 A251727 KEYWORD nonn AUTHOR Antti Karttunen, Dec 15 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)