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

Author

Lei Zhou, Aug 17 2020

Keywords

• base
• nonn

Comments

Sign nonadjacent form notation is defined by the publications listed in the reference.

We use abbreviation SNF for "signed nonadjacent form" notation.

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.

Crossrefs

Cf. A334913, A337123.

Programs

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}]