A140327 a(0)=1. For n >=1, a(n) is the smallest prime that is > a(n-1) and equals n*k -1, for some positive integer k.

1, 2, 3, 5, 7, 19, 23, 41, 47, 53, 59, 109, 131, 181, 223, 239, 271, 373, 431, 569, 599, 797, 857, 919, 983, 1049, 1091, 1187, 1231, 1913, 1949, 2293, 2399, 2441, 2447, 2659, 2663, 3181, 3191, 3821, 3919, 4099, 4157, 4643, 4663, 4679, 4691, 4793, 4799, 4801

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

The numbers of the form 7*k - 1 that are greater than a(6) = 23 form the sequence that starts 27,34,41,48,... The first prime of this sequence is 41. So a(7) = 41.

Maple

A140327 := proc(n) option remember ; local a, k ; if n = 0 then 1; else for a from A140327(n-1)+1 do if isprime(a) then for k from 0 do if a = n*k-1 then RETURN(a) ; elif n*k-1 > a then break ; fi ; od: fi ; od: fi ; end: seq(A140327(n), n=0..80) ; # R. J. Mathar, Jun 19 2008

Mathematica

nxt[{n_, a_}]:=Module[{k=Floor[a/(n+1)]+1, lst}, lst=(n+1)Range[k, k+50]-1; {n+1, SelectFirst[lst, #>a&&PrimeQ[#]&]}]; NestList[nxt, {0, 1}, 60][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 01 2018 *)

Crossrefs

Cf. A071899.

Sequence in context: A332583 A345335 A025019 * A346167 A163074 A230041

Adjacent sequences: A140324 A140325 A140326 * A140328 A140329 A140330

Keyword

nonn

Author

Leroy Quet, May 26 2008

Extensions

More terms from R. J. Mathar, Jun 19 2008

Status

approved