

A123375


Least k such that the difference between consecutive semiprimes A065516(k) equals n, or 0 if no such k exists.


5



3, 1, 2, 4, 24, 6, 10, 56, 50, 78, 34, 320, 249, 186, 463, 762, 598, 1238, 422, 760, 3760, 3585, 9214, 1765, 4112, 13447, 6675, 4585, 68498, 8112, 10083, 8650, 86203, 49433, 35085, 20641, 458421, 8861, 366314, 157857, 169147, 487115, 277440
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OFFSET

1,1


COMMENTS

a(n) equals least k such that A065516(k) = n, or 0 if no such k exists. Conjecture: a(n)>0 exists for all n.


LINKS

Table of n, a(n) for n=1..43.
Eric Weisstein's World of Mathematics, Semiprime


EXAMPLE

A065516(n) begins {2, 3, 1, 4, 1, 6, 1, 3, 1, 7, 1, 1, 3, 1, 7, 3, 2, 4, 2, 1, 4, 3, 4, 5, ...}.
Thus a(1) = 3, a(2) = 1, a(3) = 2, a(4) = 4, a(5) = 24.


MAPLE

nextSprime := proc(n) local res ; res := n+1 ; while numtheory[bigomega](res) <> 2 do res := res+1 ; od ; RETURN(res) ; end ; nmax := 500 ; kmax := 500000 ; a := array(1..nmax) ; for i from 1 to nmax do a[i] := 0 ; od : sp1 := 4 : sp2 := nextSprime(sp1) : n := sp2sp1 : a[n] := 1 : for k from 2 to kmax do sp1 := sp2 ; sp2 := nextSprime(sp1) ; n := sp2sp1 ; if a[n] = 0 then a[n] := k ; fi ; od : for i from 1 to nmax do if a[i] = 0 then break ; else printf("%d, ", a[i]) ; fi ; od : # R. J. Mathar, Jan 13 2007


CROSSREFS

Cf. A001358  Semiprimes. Cf. A065516  Differences between semiprimes.
Sequence in context: A230892 A325671 A138382 * A021036 A211025 A125704
Adjacent sequences: A123372 A123373 A123374 * A123376 A123377 A123378


KEYWORD

hard,nonn


AUTHOR

Alexander Adamchuk, Nov 09 2006


EXTENSIONS

Corrected and extended by R. J. Mathar, Jan 13 2007


STATUS

approved



