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A114412 Records in semiprime gaps ordered by merit. 16
2, 3, 4, 6, 11, 19, 24, 28, 30, 32, 38, 47, 54, 70, 74, 107, 110, 112, 120, 126, 146 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There is an associated index list n = 1, 2, 4, 6, 34, 422, 1765, 4585, 8112, 8650, 8861, 75150, ... and an associated semiprime list A001358(n) = 4, 6, 10, 15, 1418, 6559, 17965, 32777, 35103, 35981, 340894, ... - R. J. Mathar, Mar 15 2009
LINKS
Eric Weisstein's World of Mathematics, Semiprime.
Eric Weisstein's World of Mathematics, Prime Gaps.
FORMULA
a(n) = records in A065516/log(A001358(n)) = records in (A001358(n+1) - A001358(n))/log(A001358(n))).
EXAMPLE
Records defined in terms of A065516 and A001358:
.
n A065516(n) A065516(n)/log_10(A001358(n))
= ========== ==============================
1 2 2 / log_10(4) = 3.32192809...
2 3 3 / log_10(6) = 3.85529162...
3 1 1 / log_10(9) = 1.04795163...
4 4 4 / log_10(10) = 4.00000000
5 1 1 / log_10(14) = 0.87250286...
6 6 6 / log_10(15) = 5.10164492...
7 1 1 / log_10(21) = 0.75630419...
8 3 3 / log_10(22) = 2.23476557...
9 1 1 / log_10(25) = 0.71533827...
MATHEMATICA
sp = 4; m0 = 0; l = {}; lim = 1000000;
For[i = 5, i <= lim, i++, If[PrimeOmega[i] == 2, m = (i - sp)/Log[sp]; If[m > m0, m0 = m; AppendTo[l, i - sp]]; sp = i] ]; l (* Robert Price, Oct 29 2018 *)
CROSSREFS
Sequence in context: A111124 A295681 A117308 * A352819 A016038 A003099
KEYWORD
nonn,more
AUTHOR
Jonathan Vos Post, Nov 25 2005
EXTENSIONS
Corrected and extended by Charles R Greathouse IV, Oct 05 2006
a(16)-a(21) from Donovan Johnson, Feb 17 2010
STATUS
approved

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Last modified March 19 02:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)