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A164918 The smallest starting prime which reaches prime(n) by repeated application of the map x->A060308(x). 4
2, 2, 2, 2, 11, 2, 17, 11, 2, 29, 17, 11, 41, 2, 47, 29, 59, 17, 67, 71, 11, 41, 2, 47, 97, 101, 29, 107, 109, 17, 127, 67, 137, 11, 149, 151, 41, 2, 167, 47, 179, 181, 191, 97, 197, 29, 107, 17, 227, 229, 233, 239, 241, 127, 67, 263, 269, 137, 11, 281, 283, 149, 307, 311, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the starting value of the prime chain described in A164917 which contains (touches) prime(n).

By construction, each member of this sequence here is one of the values of A164368, the head elements of all chains of this map.

LINKS

Table of n, a(n) for n=1..65.

V. Shevelev, On critical small intervals containing primes, arXiv:0908.2319 [math.NT], 2009.

EXAMPLE

The first four values are 2 because prime(1)=2, prime(2)=3, prime(3)=5 and prime(4)=7 are all in the prime chain starting at 2.

MAPLE

A060308 := proc(n) prevprime(2*n+1) ; end:

isA164368 := proc(p) local q ; q := nextprime(floor(p/2)) ; return (numtheory[pi](2*q) -numtheory[pi](p) >= 1); end proc:

A164368 := proc(n) option remember; local a; if n = 1 then 2; else a := nextprime( procname(n-1)) ; while not isA164368(a) do a := nextprime(a) ; end do : RETURN(a) ; end if; end proc:

A164918 := proc(n) local p, a, j, q, itr ; p := ithprime(n) ; a := 1000000000000000 ; for j from 1 do q := A164368(j) ; if q > p then break; end if; itr := 0 ; while q < p do q := A060308(q) ; itr := itr+1 ; end do; if q = p then return A164368(j) ; end if; end do: end proc:

seq(A164918(n), n=1..120) ; # R. J. Mathar, Mar 12 2010

MATHEMATICA

lp[n_] := NextPrime[2n, -1];

a[n_] := For[pn = Prime[n]; p = 2, p <= pn, p = NextPrime[p], nwl = NestWhileList[lp, p, # <= Prime[n]&]; If[MemberQ[nwl, pn], Return[p]]];

Array[a, 120] (* Jean-Fran├žois Alcover, Dec 01 2017 *)

CROSSREFS

Cf. A006992, A164917, A104272, A164368, A164288.

Sequence in context: A175392 A289910 A112727 * A147822 A316497 A084961

Adjacent sequences:  A164915 A164916 A164917 * A164919 A164920 A164921

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Aug 31 2009

EXTENSIONS

Edited and extended by R. J. Mathar, Mar 12 2010

STATUS

approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)