The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A066352 Pillai sequence: a(n) is the smallest term in A007924 requiring n primes. 9
 0, 1, 4, 27, 1354, 401429925999155061 (list; graph; refs; listen; history; text; internal format)
 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. 159-167. LINKS Florian Luca and Ravindranathan Thangadurai, On an arithmetic function considered by Pillai, Journal de théorie des nombres de Bordeaux 21:3 (2009), pp. 695-701. M. T. Marcos, Smarandache Prime Base representation, prime puzzle 141. Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101] FORMULA a(n) = 2*p(m) - p(m-1) with minimal m = pi(a(n)) so that p(m) = a(n-1) + p(m-1), where p(n) is A008578(n). EXAMPLE The greatest prime <= 27 is 23; the greatest prime <= 27-23 is 3; 27-23-3 = 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(n-precprime(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: A271385 A347146 A110763 * A249105 A249110 A348329 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

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

Last modified September 27 13:08 EDT 2022. Contains 357057 sequences. (Running on oeis4.)