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%I #8 Sep 20 2020 00:33:07
%S 0,0,0,0,3,4,7,4,8,8,12,7,11,6,11,9,13,9,18,10,21,7,9,11,16,4,8,9,7,
%T 12,18,12,14,11,10,9,18,7,12,10,18,12,22,5,11,13,16,13,22,8,9,16,13,9,
%U 13,14,10,11,10,10,20,14,9,10,13,8,22,10,10,10,12,13
%N a(n) is the number of primes p in the n-digit "signed nonadjacent form" such that p has three nonzero digits.
%C Sign nonadjacent form notation is defined by the publications listed in the reference.
%C We use abbreviation SNF for "signed nonadjacent form" notation.
%D Joerg Arndt, Matters Computational - Ideas, Algorithms, Source Code, 2011, Springer, pp. 61-62.
%H H. Prodinger, <a href="http://www.emis.de/journals/INTEGERS/papers/a8/a8.Abstract.html">On binary representations of integers with digits -1,0,1</a>, Integers 0 (2000), #A08.
%e It needs at least 5 digits to have three or more nonzero digits in SNF notation. So a(1)=a(2)=a(3)=a(4)=0.
%e In 5-digit SNF numbers, 10T0T = 11 base 10, 10T01 = 13, and 10101 = 19 are primes with three nonzero digits in SNF notation. So a(5)=3. Another prime with 5 SNF digits, 10001 = 17 has only 2 SNF digits, so is excluded.
%t Table[s1=2^(n-1);ct=0; If[n>=5, Do[s2=2^i; If[PrimeQ[s1+s2+1],ct++]; If[PrimeQ[s1+s2-1],ct++]; If[PrimeQ[s1-s2+1],ct++]; If
%t [PrimeQ[s1-s2-1],ct++], {i,2,n-3}]]; ct, {n,1,73}]
%Y Cf. A334913, A337123.
%K base,nonn
%O 1,5
%A _Lei Zhou_, Aug 17 2020
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