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Numbers k such that 2^k + 35 is prime.
7

%I #25 Nov 27 2023 15:06:55

%S 1,3,5,7,9,11,15,25,33,57,117,133,189,195,263,273,287,509,693,1087,

%T 1145,1159,1845,2743,3275,12223,26263,31425,44359,48003,49251,62557,

%U 113877,114507,132865,165789,192549,348437,426043,436365,471043,480417

%N Numbers k such that 2^k + 35 is prime.

%C Some terms correspond to probable primes. Lifchitz link shows Lelio R Paula found the terms 132865, 165789, 192549, 348437. - _Jens Kruse Andersen_, Oct 01 2014

%C a(43) > 5*10^5. - _Robert Price_, Nov 01 2015

%C All terms are odd. - _Elmo R. Oliveira_, Nov 27 2023

%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=2^n%2B35">Search for 2^n+35</a>, PRP Top Records.

%t Select[Range[5000],PrimeQ[2^# + 35] &]

%o (PARI) for(n=1, 10^30, if (isprime(2^n + 35), print1(n", "))); \\ _Altug Alkan_, Oct 05 2015

%Y Cf. A094076, A176927.

%Y Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1; A057732 (d=3), A059242 (d=5), A057195 (d=7), A057196 (d=9), A102633 (d=11), A102634 (d=13), A057197 (d=15), A057200 (d=17), A057221 (d=19), A057201 (d=21), A057203 (d=23), A157006 (d=25), A157007 (d=27), A156982 (d=29), A247952 (d=31), A247953 (d=33), this sequence (d=35).

%K nonn

%O 1,2

%A _Vincenzo Librandi_, Dec 04 2012

%E a(26)-a(34) from _Jens Kruse Andersen_, Oct 01 2014

%E 132865, 165789, 192549, 348437 discovered by Lelio R Paula confirmed as a(35)-a(38) by _Robert Price_, Oct 05 2015

%E a(39)-a(42) from _Robert Price_, Nov 01 2015