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%I #51 Jul 13 2023 01:16:48
%S 1,1,1,2,1,1,2,1,1,2,1,3,2,1,1,4,2,1,2,1,1,2,1,5,2,1,3,2,1,1,8,2,1,2,
%T 1,1,4,2,1,2,1,7,2,1,3,4,2,1,2,1,1,2,1,1,2,1,7,4,5,3,4,2,1,2,1,3,2,1,
%U 1,10,3,3,2,1,1,4,2,1,4,2,1,2,1,5,2,1,3,2,1,1,4,3,3,2,1,1,2,1,1,6,5,3,6
%N a(n) is the least positive k such that (2n+1) + 2^k is prime, or 0 if no such k exists.
%C From Phil Moore (moorep(AT)lanecc.edu), Dec 14 2009: (Start)
%C It is known that a(39278) = 0, since no such prime exists for the Sierpiński number 78557 (cf. A076336).
%C It has recently been discovered that 2131+2^4583176 and 41693+2^5146295 are probable primes, so a(1065) is probably 4583176 and a(20846) is probably 5146295.
%C At present, the only odd value less than 78557 for which no prime or strong probable prime of the form t+2^k is known is t = 40291, so a(20145) is completely unknown. In addition, for 25 values of t < 78557, only strong probable primes are known. (End)
%C The last case was resolved in 2011 when the probable prime 40291+2^9092392 was found as a part of a distributed project "Five or Bust". See links. - _Jeppe Stig Nielsen_, Mar 29 2019
%H Jinyuan Wang, <a href="/A067760/b067760.txt">Table of n, a(n) for n = 0..39278</a> (terms 0..1064 from T. D. Noe, terms 1065..3000 from Richard N. Smith).
%H Mersenne Forum, <a href="https://www.mersenneforum.org/forumdisplay.php?f=86">Five or Bust</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_167.htm">Puzzle 167. Primes m + 2^j & m - 2^j</a>, The Prime Puzzles and Problems Connection.
%e a(15)=4 because (2*15+1)+2^k is composite for k=1,2,3 and prime for k=4.
%o (PARI) a(n) = {my(k=1); while (! isprime((2*n+1)+2^k), k++); k;} \\ _Michel Marcus_, Feb 26 2018
%Y Cf. A016014, A050412, A066081, A033919, A094076, A076336, A260350, A263874, A263875 (records).
%K nonn
%O 0,4
%A _Don Reble_, Feb 05 2002
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