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

1,5

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

Table of n, a(n) for n=1..72.

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