

A066352


Pillai sequence: a(n) is the smallest term in A007924 requiring n primes.


9




OFFSET

0,3


COMMENTS

a(5) computed independently in 2007 by R. J. Mathar and Luca & Thangadurai, both using Thomas Nicely's tables.
On Cramer's conjecture, the number of primes required is O(log* n), where log* is the iterated logarithm, so the rate of growth of a(n) is tetrational in n.  Charles R Greathouse IV, Aug 28 2010
The next term likely has hundreds of millions of digits.  Charles R Greathouse IV, Jun 29 2015


REFERENCES

S. S. Pillai, "An arithmetical function concerning primes", Annamalai University Journal (1930), pp. 159167.


LINKS

Table of n, a(n) for n=0..5.
Florian Luca and Ravindranathan Thangadurai, On an arithmetic function considered by Pillai, Journal de thÃ©orie des nombres de Bordeaux 21:3 (2009), pp. 695701.
M. T. Marcos, Smarandache Prime Base representation, prime puzzle 141.
Thomas R. Nicely, First occurrence prime gaps


FORMULA

a(n) = 2*p(m)  p(m1) with minimal m = pi(a(n)) so that p(m) = a(n1) + p(m1), where p(n) is A008578(n).


EXAMPLE

The greatest prime <= 27 is 23; the greatest prime <= 2723 is 3; 27233 = 1, so the Pillai representation of 27 is 23+3+1, which uses more terms than all preceding numbers.


PROG

(PARI) A072491(n)=if(n<4, n>0, 1+A072491(nprecprime(n)))
print1(r=0); for(n=1, 1e7, if(A072491(n)>r, r=a(n); print1(", "n)))
\\ Charles R Greathouse IV, Feb 04 2013


CROSSREFS

Cf. A007924.
Sequence in context: A133032 A271385 A110763 * A249105 A249110 A051674
Adjacent sequences: A066349 A066350 A066351 * A066353 A066354 A066355


KEYWORD

nonn,hard


AUTHOR

Copied from www.primepuzzles.net by Frank Ellermann, Dec 19 2001


EXTENSIONS

Edited by Charles R Greathouse IV, Oct 28 2009
Entry rewritten by Charles R Greathouse IV, Aug 28 2010


STATUS

approved



