

A261577


Numbers m such that (4^m + 11) / 3 is prime.


1



1, 4, 10, 34, 40, 106, 418, 682, 12702, 30484, 182026, 217720, 241306
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OFFSET

1,2


COMMENTS

After 1, m is always even (for m odd 4^m+11 is divisible by 5).
Let m = 2*h. For h = 3*k+1, 9*k+3, 11*k+2, 11*k+8, 13*k+8, 19*k+6, 23*k+10, 23*k+14 and 29*k+28, 4^m+11 is divisible by 9, 37, 89, 23, 53, 229, 47, 1013 and 59, respectively. (End)
All terms appear to be of the form 3*k+1.  Dhilan Lahoti, Aug 31 2015
12702 is the first counterexample to Dhilan Lahoti's conjecture: 12702 = 3*4234.  Bruno Berselli, Feb 02 2017


LINKS



EXAMPLE

4 is in the sequence because (4^4+11)/3 = 89 is prime.
10 is in the sequence because (4^10+11)/3 = 349529 is prime.


MATHEMATICA

Select[Range[0, 5000], PrimeQ[(4^# + 11)/3] &]


PROG

(Magma) [n: n in [0..1500]  IsPrime((4^n+11) div 3)];


CROSSREFS

Cf. similar sequences listed in A261539.


KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



