A095906 -id:A095906 - cp's OEIS frontend

A082103 Numbers n such that 3^n + 2^(n-1) is prime.

2, 3, 4, 6, 7, 8, 10, 15, 21, 24, 36, 49, 51, 86, 116, 134, 176, 284, 345, 498, 544, 649, 844, 1051, 1171, 1384, 1497, 1514, 1638, 1856, 2860, 2890, 3235, 3584, 4047, 5990, 7729, 8935, 9907, 15241, 15864, 17629, 19264, 28239, 43730, 46879, 65379, 89468, 128787, 139976

Offset: 1

Labos Elemer, Apr 14 2003

nonn

a(51) > 2*10^5. - Robert Price, May 06 2016

			n=4: 89 = 2*2*2 + 3*3*3*3 is prime.
n=15: 3^15 + 2^14 = 14365291 is prime.

Cf. A082101, A082102, A095906, A093717, A093793, A093765, A096185, A093794, A093795, A096186.

[n: n in [0..1000] | IsPrime(3^n + 2^(n-1))]; // Vincenzo Librandi, Mar 20 2015

Do[ If[ PrimeQ[3^n + 2^(n - 1)], Print[n]], {n, 7650}] (* Robert G. Wilson v, May 24 2004 *)
Select[Range[6000], PrimeQ[3^# + 2^(#-1)] &] (* Vincenzo Librandi, Mar 20 2015 *)

is(n)=isprime(3^n+2^(n-1)) \\ Charles R Greathouse IV, Feb 17 2017

Edited and extended by Robert G. Wilson v, May 25 2004
Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar
a(37)-a(50) from Robert Price, May 06 2016

A094679 n sets a new record for number of iterations to reach 1 in the juggler sequence problem.

Original entry on oeis.org

1, 2, 3, 9, 19, 25, 37, 77, 163, 193, 1119, 1155, 4065, 4229, 4649, 7847, 13325, 34175, 59739, 78901, 636731, 1122603, 1301535, 2263913, 5947165, 72511173, 78641579, 125121851, 198424189, 4488817391

Offset: 1

Jason Earls, Jun 09 2004

Where records occur in A007320.
The Juggler sequence: begin with x and if x is even, [sqrt(x)] -> x and if x is odd, [sqrt(x^3)] -> x and repeat until x = 1, count the iterations. - Robert G. Wilson v, Jun 14 2004
78901 reaches a maximum of 4064983429...(skip the next 371727 digits)...2140697134 during its trip to 1. - Robert G. Wilson v, Jun 14 2004
I postulate that 2 is the only even number in this sequence. - Harry J. Smith, Aug 15 2008
a(30) > 1.6*10^9. - Giovanni Resta, Apr 08 2017

			78901 takes 258 iterations to reach 1; see A094698 for the others.

Eric Weisstein's World of Mathematics, Juggler Sequence

Cf. A007320, A094670, A094698, A095906, A094698.

$MaxPrecision = 250000000; js[n_] := If[ EvenQ[ n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Block[{c = 1, k = n}, While[k = js[k]; k != 1, c++ ]; c]; a = {0}; Do[ b = f[n]; If[b > a[[ -1]], AppendTo[a, b]], {n, 3053595}]; a (* Robert G. Wilson v *)

More terms from Robert G. Wilson v, Jun 14 2004
a(25) = 5947165 from Eric W. Weisstein, Jan 25 2006
a(26)-a(27) from Robert G. Wilson v, Jun 15 2014
a(28)-a(29) from Giovanni Resta, Apr 08 2017
a(30) from Ethan Slota, Apr 15 2025

cp's OEIS Frontend

A082103 Numbers n such that 3^n + 2^(n-1) is prime.

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