A001632 Smallest prime p such that there is a gap of 2n between p and previous prime.

5, 11, 29, 97, 149, 211, 127, 1847, 541, 907, 1151, 1693, 2503, 2999, 4327, 5623, 1361, 9587, 30631, 19373, 16183, 15727, 81509, 28277, 31957, 19661, 35671, 82129, 44351, 43391, 34123, 89753, 162209, 134581, 173429, 31469, 404671, 212777

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

Smallest prime preceded by 2n-1 successive composites. - Lekraj Beedassy, Apr 23 2010

Examples

			The first time a gap of 4 occurs between primes is between 7 and 11, so A000230(2)=7 and A001632(2)=11.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 97, p. 34, Ellipses, Paris 2008.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..595 (from Nicely)
• L. J. Lander and T. R. Parkin, On the first appearance of prime differences, Math. Comp., 21 (1967), 483-488.
• Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
• Index entries for primes, gaps between

Crossrefs

Cf. A000230, A002386.

Programs

Mathematica

With[{pr=Partition[Prime[Range[35000]],2,1]},Transpose[ Flatten[ Table[ Select[pr,#[[2]]-#[[1]]==2n&,1],{n,40}],1]][[2]]] (* Harvey P. Dale, Apr 20 2012 *)

PARI

LIMIT=10^9; a=[]; i=2; o=2; g=0; forprime(p=3,LIMIT, bittest(g,-o+o=p) && next; a=concat(a,[[p,p-precprime(p-1)]]); g+=1<=i && a[i][2]<2*i, print1(a[i][1]",");i++)) \\ a[1] = [3, 1] is not printed, cf. A000230(0). Limit 10^7 yields a(1),...,a(70) in 0.3 sec @ 2.5 GHz. \\ M. F. Hasler, Jan 13 2011, updated Jan 26 2015.

Formula

a(n) = 2n + A000230(n) = nextprime(A000230(n)).

a(n) = A000040(A038664(n)+1). - M. F. Hasler, Jan 26 2015

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Nov 28 2000 and from Labos Elemer, Nov 29 2000

Terms a(1)-a(146) checked with the PARI program by M. F. Hasler, Jan 13 2011, Jan 26 2015