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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

print1(w=2);p=2;q=3;forprime(r=5,1e9,if(p+w+ww,w=t;print1(", "t));p=q;q=r) \\ Charles R Greathouse IV, Jan 16 2012

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

Extensions

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

Further terms from Naohiro Nomoto, Jun 21 2001