cp's OEIS Frontend

A057196 Numbers k such that 2^k + 9 is prime.

%I A057196 #34 Mar 17 2025 07:24:52
%S A057196 1,2,3,5,6,7,9,10,18,23,30,37,47,57,66,82,95,119,175,263,295,317,319,
%T A057196 327,670,697,886,1342,1717,1855,2394,2710,3229,3253,3749,4375,4494,
%U A057196 4557,5278,5567,9327,10129,12727,13615,14893,16473,23639,40053,44399,50335,80949
%N A057196 Numbers k such that 2^k + 9 is prime.
%C A057196 Some of the larger terms are only probable primes.
%C A057196 For these numbers k, 2^(k-1)*(2^k+9) has deficiency 10 (see A101223). - _M. F. Hasler_, Jul 18 2016
%C A057196 The terms a(48)-a(51) were found by Mike Oakes, a(52) found by Gary Barnes, and a(53-56) found by Lelio R Paula (see link Henri Lifchitz and Renaud Lifchitz). - _Elmo R. Oliveira_, Dec 01 2023
%H A057196 Robert Price, <a href="/A057196/b057196.txt">Table of n, a(n) for n = 1..56</a>
%H A057196 Keith Conrad, <a href="https://kconrad.math.uconn.edu/blurbs/ugradnumthy/squaresandinfmanyprimes.pdf">Square patterns and infinitude of primes</a>, University of Connecticut, 2019.
%H A057196 Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En%2B9">Search for 2^n+9</a>, PRP Top Records.
%e A057196 For k = 10, 2^10 + 9 = 1033 is prime.
%e A057196 For k = 30, 2^30 + 9 = 1073741833 is prime.
%t A057196 Do[ If[ PrimeQ[ 2^n +9 ], Print[n]], { n, 1, 15000 }]
%o A057196 (PARI) for(n=1, oo, ispseudoprime(2^n+9)&&print1(n", ")) \\ _M. F. Hasler_, Jul 18 2016
%Y A057196 Cf. A094076, A101223, A104070 (primes of the form 2^k+9). [_Klaus Brockhaus_, Mar 14 2009]
%Y A057196 Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), this sequence (2^k+9), A102633 (2^k+11), A102634 (2^k+13), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23). [_M. F. Hasler_, Jul 18 2016]
%K A057196 nonn
%O A057196 1,2
%A A057196 _Robert G. Wilson v_, Sep 15 2000
%E A057196 a(48)-a(51) from _Mike Oakes_, Aug 17 2001
%E A057196 Edited by _T. D. Noe_, Oct 30 2008