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A121885 Excess of n-th prime over previous semiprime. 2
1, 1, 1, 3, 2, 4, 1, 3, 5, 2, 2, 4, 1, 2, 1, 3, 2, 2, 4, 2, 1, 2, 2, 6, 8, 1, 3, 2, 4, 2, 3, 5, 3, 5, 2, 2, 1, 4, 1, 3, 4, 6, 3, 5, 2, 2, 1, 3, 7, 2, 4, 2, 3, 1, 2, 4, 3, 3, 5, 2, 2, 2, 4, 3, 2, 2, 1, 3, 7, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 4, 4, 6, 2, 6, 2, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,4

COMMENTS

See: A102415 Greatest semiprime less than n-th prime. See: A102414 Smallest semiprime greater than n-th prime.

LINKS

T. D. Noe, Table of n, a(n) for n = 3..10000

FORMULA

a(n) = Min{A000040(n)-s for s < A000040(n) and s in A001358(k)}. a(n) = A000040(n) - A102415(n).

MATHEMATICA

SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Table[i = Prime[n] - 1; While[! SemiPrimeQ[i], i--]; Prime[n] - i, {n, 3, 100}] (* T. D. Noe, Oct 08 2012 *)

eps[n_]:=Module[{c=n-1}, While[PrimeOmega[c]!=2, c--]; n-c]; Table[eps[n], {n, Prime[Range[3, 90]]}] (* Harvey P. Dale, Aug 12 2014 *)

PROG

(PARI) dsemi(n)= { local(k=0); if(isprime(n), k=0; while(bigomega(n-k)<>2&&k<n, k=k+1)); return(k) }

{ forprime(n=5, 10^3, print(n, " ", dsemi(n))) } // Antonio Roldán, Oct 08 2012

CROSSREFS

Cf. A000040, A001358, A062721, A077068, A102414, A102415.

Sequence in context: A226377 A140430 A123359 * A187760 A122143 A144868

Adjacent sequences:  A121882 A121883 A121884 * A121886 A121887 A121888

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 31 2006

EXTENSIONS

Extended by T. D. Noe, Oct 08 2012

STATUS

approved

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)