The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A049076 Number of steps in the prime index chain for the n-th prime. 63
 1, 2, 3, 1, 4, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let p(k) = k-th prime, let S(p) = S(p(k)) = k, the subscript of p; a(n) = order of primeness of p(n) = 1+m where m is largest number such that S(S(..S(p(n))...)) with m S's is a prime. The record holders correspond to A007097. LINKS N. Fernandez, Table of n, a(n) for n = 1..500 N. Fernandez, An order of primeness, F(p) N. Fernandez, An order of primeness [cached copy, included with permission of the author] N. Fernandez, The Exploring Primeness Project FORMULA Let b(n) = 0 if n is nonprime, otherwise b(n) = k where n is the k-th prime. Then a(n) is the number of times you can apply b to the n-th prime before you hit a nonprime. a(n) = 1 + A078442(n). - R. J. Mathar, Jul 07 2012 a(n) = A078442(A000040(n)). - Alois P. Heinz, Mar 16 2020 EXAMPLE 11 is 5th prime, so S(11)=5, 5 is 3rd prime, so S(S(11))=3, 3 is 2nd prime, so S(S(S(11)))=2, 2 is first prime, so S(S(S(S(11))))=1, not a prime. Thus a(5)=4. Alternatively, a(5) = 4: the 5th prime is 11 and its prime index chain is 11->5->3->2->1->0. a(6) = 1: the 6th prime is 13 and its prime index chain is 13->6->0. MAPLE A049076 := proc(n)     if not isprime(n) then         1 ;     else         1+procname(numtheory[pi](n)) ;     end if; end proc: seq(A049076(n), n=1..30) ; # R. J. Mathar, Jan 28 2014 MATHEMATICA A049076 f[n_] := Length[ NestWhileList[ PrimePi, n, PrimeQ]]; Table[ f[n], {n, 105}] (* Robert G. Wilson v, Mar 11 2004 *) Table[Length[NestWhileList[PrimePi[#]&, Prime[n], PrimeQ[#]&]]-1, {n, 110}] (* Harvey P. Dale, May 07 2018 *) PROG (PARI) apply(p->my(s=1); while(isprime(p=primepi(p)), s++); s, primes(100)) \\ Charles R Greathouse IV, Nov 20 2012 (Haskell) a049076 = (+ 1) . a078442  -- Reinhard Zumkeller, Jul 14 2013 CROSSREFS Cf. A000040, A049077 - A049081, A006450, A049084, A236542. Sequence in context: A268727 A325542 A081877 * A097744 A055445 A135560 Adjacent sequences:  A049073 A049074 A049075 * A049077 A049078 A049079 KEYWORD nice,nonn,easy AUTHOR EXTENSIONS Additional comments from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 12 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 23:47 EST 2020. Contains 338685 sequences. (Running on oeis4.)