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A065380 Primes of the form p + 2^k, p prime and k >= 0. 4

%I #17 Nov 21 2013 12:47:34

%S 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,

%T 101,103,107,109,113,131,137,139,151,157,163,167,173,179,181,191,193,

%U 197,199,211,223,227,229,233,239,241,257,263,269,271,277,281,283,293

%N Primes of the form p + 2^k, p prime and k >= 0.

%H Reinhard Zumkeller, <a href="/A065380/b065380.txt">Table of n, a(n) for n = 1..10000</a>

%F A078687(A049084(a(n))) > 0; A091932 is a subsequence. - _Reinhard Zumkeller_, May 07 2006

%e a(3) = 11 = 3 + 2^3 = 7 + 2^2.

%t With[{upto=300},Select[Union[Select[Flatten[Outer[Plus,Prime[Range[ PrimePi[upto]]],2^Range[0,Floor[Log[2,upto]]]]],PrimeQ]],#<=upto&]] (* _Harvey P. Dale_, Feb 28 2012 *)

%o (Haskell)

%o a065380 n = a065380_list !! (n-1)

%o a065380_list = filter f a000040_list where

%o f p = any ((== 1) . a010051 . (p -)) $ takeWhile (<= p) a000079_list

%o -- _Reinhard Zumkeller_, Nov 24 2011

%Y Cf. A010051, A000079, A065381, A156695.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Nov 03 2001

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)