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 A091987 Number of steps required for initial p = 2^n to reach 0 in the recurrence p = pi(p). 0
 1, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Andrew Booker, The Nth Prime Page. FORMULA pi(n) = A000720(n) = number of primes less than or equal to n. By repeating n=pi(n), n will reach 0 in a finite number of steps. EXAMPLE Pi(32) = 11 Pi(11) = 5 Pi(5) = 3 Pi(3) = 2 Pi(2) = 1 Pi(1) = 0 Total steps to reach 0 = 6. Thus 6 is the 6th entry in the sequence corresponding to n=5. MATHEMATICA Table[Length[NestWhileList[PrimePi, 2^n, #>0&]]-1, {n, 0, 40}] (* Harvey P. Dale, May 29 2016 *) PROG (PARI) pr2n(n) = my(c); for(x=0, n, y=2^x; c=0; p=y; while(p, p = primepi(p); c++); print1(c", ")) CROSSREFS Cf. A000720. Sequence in context: A097622 A236561 A110010 * A025544 A327706 A121856 Adjacent sequences:  A091984 A091985 A091986 * A091988 A091989 A091990 KEYWORD hard,nonn AUTHOR Cino Hilliard, Mar 16 2004 EXTENSIONS More terms from Harvey P. Dale, May 29 2016 a(41)-a(64) from Chai Wah Wu, May 25 2018 STATUS approved

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Last modified January 25 04:15 EST 2022. Contains 350565 sequences. (Running on oeis4.)