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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
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.
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
Sequence in context: A282535 A193967 A109823 * A267447 A071051 A212807
KEYWORD
base,nonn
AUTHOR
Lei Zhou, Aug 17 2020
STATUS
approved