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A152073 a(n) = largest prime < prime(n) such that prime(n) - a(n) is a power of 2, where prime(n) is the n-th prime; a(n) = 0 if no such prime exists.

%I A152073 #19 Sep 05 2019 10:33:59
%S A152073 2,3,5,7,11,13,17,19,13,29,29,37,41,43,37,43,59,59,67,71,71,79,73,89,
%T A152073 97,101,103,107,109,0,127,73,137,0,149,149,131,163,157,163,179,127,
%U A152073 191,193,197,179,191,223,227,229,223,239,0,241,199,13,269,269,277,281,277,179
%N A152073 a(n) = largest prime < prime(n) such that prime(n) - a(n) is a power of 2, where prime(n) is the n-th prime; a(n) = 0 if no such prime exists.
%C A152073 a(n) = 0 for odd primes prime(n) appearing in A065381.
%C A152073 Primes p(n) for which there is no such prime a(n) (in which case a(n)=0) are listed in A065381 = (2,127,149,251,331,337,373,...). - _M. F. Hasler_, Nov 23 2008
%H A152073 Ivan Neretin, <a href="/A152073/b152073.txt">Table of n, a(n) for n = 2..10000</a>
%e A152073 Looking at the primes less than the 10th prime = 29: 29 - 23 = 6, not a power of 2. 29-19 = 10, not a power of 2. 29-17 = 12, not a power of 2. But 29-13 = 16, a power of 2. Since p = 13 is the largest prime p such that 29 - p = a power of 2, then a(10) = 13.
%t A152073 Table[Max[0, Select[# - 2^Range[0, Log2@#] &@Prime[n], PrimeQ]], {n, 2, 63}] (* _Ivan Neretin_, Jun 10 2018 *)
%o A152073 (PARI) A152073(n)=local( q=n=prime(n)); while( q=precprime(q-1), n-q==1<<valuation(n-q,2) && return(q)) \\ _M. F. Hasler_, Nov 23 2008
%Y A152073 Cf. A065381, A139758, A152075, A152076, A156695.
%K A152073 nonn,look
%O A152073 2,1
%A A152073 _Leroy Quet_, Nov 23 2008
%E A152073 Edited and extended by _M. F. Hasler_ and _Ray Chandler_, Nov 23 2008