A051730 Distance from A051650(n) to nearest prime.

2, 4, 6, 7, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 30, 31, 32, 33, 34, 35, 36, 40, 42, 43, 44, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..211 (calculated from the b-file at A051650)

Example

23 is 4 units away from the closest prime (not including itself), so 4 is in the sequence.

Mathematica

(* b stands for A051650 *) d[0] = 2; d[k_] := Min[k - NextPrime[k, -1], NextPrime[k] - k]; b[0] = 0; b[n_] := b[n] = (k = b[n-1] + 1; record = d[b[n-1]]; While[d[k] <= record, k++]; k); a[n_] := a[n] = d[b[n]]; Table[ Print[ a[n]]; a[n], {n, 0, 66}] (* Jean-François Alcover, Jan 16 2012 *)

Prog

(UBASIC) [10] C#=pack(3, 5):R=2:N=4:print 2; [20] if N>member(C#, 2) then C#=pack(member( C#, 2)):C#=C#+nxtprm(member(C#, 1)) [30] Prv=member(C#, 1):Nxt=member(C#, 2) [40] if Nxt=N then Nxt=nxtprm(N) [50] if (N-Prv)>=(Nxt-N) then P=Nxt-N else P=N-Prv [60] if P>R then print P; :R=P [70] N+=1 :goto 20
(PARI) print1(w=2); p=2; q=3; forprime(r=5, 1e9, if(p+w+w<q, for(t=w+1, (q-p)\2, print1(", "t)); w=(q-p)\2); t=min(q-p, r-q); if(t>w, w=t; print1(", "t)); p=q; q=r) \\ Charles R Greathouse IV, Jan 16 2012

Crossrefs

Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.

Sequence in context: A328068 A263084 A029501 * A070317 A138398 A086781

Adjacent sequences: A051727 A051728 A051729 * A051731 A051732 A051733

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Dec 23 1999 and from Jud McCranie, Jun 16 2000

Further terms from Naohiro Nomoto, Jun 21 2001

Status

approved