A337124 a(n) is the number of primes p in the n-digit "signed nonadjacent form" such that p has three nonzero digits.
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
Examples
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.
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.
Programs
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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}]
Comments