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#10 by Harvey P. Dale at Mon Aug 02 18:52:30 EDT 2021
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#9 by Harvey P. Dale at Mon Aug 02 18:52:28 EDT 2021
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| MATHEMATICA
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Select[Floor[Prime[Range[500]]^Pi], PrimeQ] (* Harvey P. Dale, Aug 02 2021 *)
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| STATUS
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approved
editing
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#8 by Susanna Cuyler at Sun Apr 11 16:13:55 EDT 2021
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#7 by Jon E. Schoenfield at Sun Apr 11 15:22:54 EDT 2021
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#6 by Jon E. Schoenfield at Sun Apr 11 15:22:42 EDT 2021
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| NAME
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Primes of the form floor(x^piPi) where x is prime.
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| EXAMPLE
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The smallest prime x for which floor(x^piPi) is prime, is 3, for which floor(3^piPi)=31, which is prime, so a(1)=31. The next smallest is 73, for which floor(73^piPi)=714169, so a(2)=714169.
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| STATUS
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approved
editing
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#5 by Russ Cox at Sat Mar 31 14:39:53 EDT 2012
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| AUTHOR
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N. _Neil Fernandez (primeness(AT)borve.org), _, Jan 27 2003
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Discussion
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Sat Mar 31
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| OEIS Server: https://oeis.org/edit/global/939
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#4 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008
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| OFFSET
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01,1
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| KEYWORD
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nonn,new
nonn
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#3 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007
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| KEYWORD
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nonn,new
nonn
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| AUTHOR
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N. Fernandez (primeness(AT)borve.demon.co.ukorg), Jan 27 2003
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#2 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004
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| KEYWORD
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nonn,new
nonn
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| AUTHOR
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Neil N. Fernandez (primeness(AT)borve.demon.co.uk), Jan 27 2003
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#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003
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| NAME
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Primes of the form floor(x^pi) where x is prime.
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| DATA
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31, 714169, 2516309, 4483363, 47127727, 145996069, 583363661, 1028282141, 1637687383, 1984271941, 3680735213, 4484951059, 5187593417, 8601029209, 19614906869, 23431992781, 33458412373, 40695658637, 41234578433
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| OFFSET
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0,1
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| EXAMPLE
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The smallest prime x for which floor(x^pi) is prime, is 3, for which floor(3^pi)=31, which is prime, so a(1)=31. The next smallest is 73, for which floor(73^pi)=714169, so a(2)=714169.
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| MATHEMATICA
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For[i = 1, i < 10000, If[PrimeQ[IntegerPart[Prime[i]^Pi]] == True, Print[IntegerPart[Prime[i]^Pi]]]; i++ ]
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| CROSSREFS
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Cf. A074218.
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| KEYWORD
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nonn
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| AUTHOR
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Neil Fernandez (primeness(AT)borve.demon.co.uk), Jan 27 2003
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| STATUS
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approved
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