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 A337124 a(n) is the number of primes p in the n-digit "signed nonadjacent form" such that p has three nonzero digits. 1
 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, 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, 13, 14, 10, 11, 10, 10, 20, 14, 9, 10, 13, 8, 22, 10, 10, 10, 12, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Sign nonadjacent form notation is defined by the publications listed in the reference. We use abbreviation SNF for "signed nonadjacent form" notation. REFERENCES Joerg Arndt, Matters Computational - Ideas, Algorithms, Source Code, 2011, Springer, pp. 61-62. LINKS H. Prodinger, On binary representations of integers with digits -1,0,1, Integers 0 (2000), #A08. EXAMPLE 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. 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. MATHEMATICA 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 [PrimeQ[s1-s2-1], ct++], {i, 2, n-3}]]; ct, {n, 1, 73}] CROSSREFS Cf. A334913, A337123. Sequence in context: A282535 A193967 A109823 * A267447 A071051 A212807 Adjacent sequences:  A337121 A337122 A337123 * A337125 A337126 A337127 KEYWORD base,nonn AUTHOR Lei Zhou, Aug 17 2020 STATUS approved

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Last modified July 26 02:10 EDT 2021. Contains 346294 sequences. (Running on oeis4.)