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A089654 Table T(n,k), read by rows, related to a conjecture of P. Erdos (see A039669).

%I A089654 #12 Apr 27 2019 05:23:00
%S A089654 1,3,1,5,3,7,5,1,9,7,3,11,9,5,13,11,7,15,13,9,1,17,15,11,3,19,17,13,5,
%T A089654 21,19,15,7,23,21,17,9,25,23,19,11,27,25,21,13,29,27,23,15,31,29,25,
%U A089654 17,1,33,31,27,19,3,35,33,29,21,5
%N A089654 Table T(n,k), read by rows, related to a conjecture of P. Erdos (see A039669).
%C A089654 row n=1 : 1
%C A089654 row n=2 : 3, 1
%C A089654 row n=3 : 5, 3
%C A089654 row n=4 : 7, 5, 1
%C A089654 row n=5 : 9, 7, 3
%C A089654 row n=6 : 11, 9, 5
%C A089654 row n=7 : 13, 11, 7
%C A089654 row n=8 : 15, 13, 9, 1
%C A089654 row n=9 : 17, 15, 11, 3
%C A089654 P. Erdos conjectures that T(n,k) are all primes for n = 3, 7, 10, 22, 37, 52 and these are the only values of n with property . The conjecture has been verified for n up to 2^77. example : n=10; 19, 17, 13, 5 are all primes.
%H A089654 P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1950-07.pdf">On integers of the form 2^k + p and some related questions</a>, Summa Bras. Math., 2 (1950), 113-123.
%F A089654 T(n, k) = 2*n+1-2^k, if T(n, k)>0.
%Y A089654 Cf. A039669.
%K A089654 easy,nonn,tabf
%O A089654 1,2
%A A089654 _Philippe Deléham_, Jan 04 2004