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A131109 a(n) is the smallest semiprime such that difference between a(n) and next semiprime, b(n), is n. 13
9, 4, 6, 10, 69, 15, 26, 169, 146, 237, 95, 1082, 818, 597, 1603, 2705, 2078, 4511, 1418, 2681, 14545, 13863, 37551, 6559, 16053, 55805, 26707, 17965, 308918, 32777, 41222, 35103, 393565, 219509, 153263, 87627, 2263057, 35981, 1789339, 741841, 797542 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is the semiprime analogous to A000230. - Robert G. Wilson v, Jun 13 2013

LINKS

T. D. Noe and Klaus Brockhaus, Table of n, a(n) for n=1..100

FORMULA

a(n) = A001358(A123375(n)) - T. D. Noe, Sep 28 2007

EXAMPLE

n, b(n)-a(n): 1=10-9, 2=6-4, 3=9-6, 4=14-10, 5=74-69, 6=21-15, 7=33-26, 8=177-169, 9=155-146, 10=247-237, 11=106-95, 12=1094-1082, 13=831-818, 14=611-597, 15=1618-1603, 16=2721-2705, 17=2095-2078, 18=4529-4511, 19=1437-1418, 20=2701-2681, 21=14566-14545, 22=13885-13863, 23=37574-37551, 24=6583-6559, 25=16078-16053, 26=55831-55805, 27=26734-26707, 28=17993-17965, 29=308947-308918, 30=32807-32777, 31=41253-41222, 32=35135-35103, 33=393598-393565, 34=219543-219509, 35=153298-153263, 36=87663-87627, 37=2263094-2263057, 38=36019-35981.

MATHEMATICA

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; NextSemiPrime[n_] := Module[{m = n + 1}, While[! SemiPrimeQ[m], m++]; m]; nn = 30; t = Table[0, {nn}]; found = 0; sp0 = 4; While[found < nn, sp1 = NextSemiPrime[sp0]; d = sp1 - sp0; If[d <= nn && t[[d]] == 0, t[[d]] = sp0; found++]; sp0 = sp1]; t (* T. D. Noe, Oct 02 2012 *)

CROSSREFS

Cf. A065516, A133478.

Sequence in context: A088539 A245084 A199054 * A267315 A247412 A154397

Adjacent sequences:  A131106 A131107 A131108 * A131110 A131111 A131112

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 24 2007

EXTENSIONS

Corrected and extended by T. D. Noe and R. J. Mathar, Sep 28 2007

STATUS

approved

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Last modified July 21 02:53 EDT 2017. Contains 289629 sequences.