A123375 Least k such that the difference between consecutive semiprimes A065516(k) equals n, or 0 if no such k exists.

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, 563951, 511757, 920602, 75150

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

David A. Corneth, Table of n, a(n) for n = 1..82

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 := sp2-sp1 : a[n] := 1 : for k from 2 to kmax do sp1 := sp2 ; sp2 := nextSprime(sp1) ; n := sp2-sp1 ; 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

Mathematica

Table[k=6; While[FreeQ[b=Differences[Select[Range@k++, PrimeOmega[#]==2&]], n]];
Length@b, {n, 11}] (* Giorgos Kalogeropoulos, Apr 02 2021 *)

Crossrefs

Cf. A001358 (semiprimes), A065516 (differences between semiprimes), A131109.

Sequence in context: A230892 A325671 A138382 * A021036 A354348 A211025

Adjacent sequences: A123372 A123373 A123374 * A123376 A123377 A123378

Keyword

nonn,hard

Author

Alexander Adamchuk, Nov 09 2006

Extensions

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

More terms from David A. Corneth, Apr 02 2021

Status

approved