A234347 a(n) = |{0 < k < n: 3^k + 3^{phi(n-k)/2} - 1 is prime}|, where phi(.) is Euler's totient function.

0, 0, 0, 1, 2, 3, 4, 3, 3, 5, 3, 5, 6, 7, 2, 6, 7, 11, 7, 3, 6, 8, 7, 4, 11, 8, 8, 6, 6, 10, 7, 6, 8, 5, 6, 4, 8, 4, 6, 6, 6, 11, 10, 3, 9, 6, 6, 4, 10, 6, 7, 3, 4, 9, 8, 9, 7, 9, 5, 9, 7, 9, 8, 4, 6, 9, 10, 7, 8, 9, 10, 5, 6, 12, 5, 6, 9, 10, 8, 9, 7, 8, 8, 10

Offset

1,5

Comments

Conjecture: a(n) > 0 for all n > 3.

See also the conjecture in A234337.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..3000

Example

a(4) = 1 since 3^1 + 3^{phi(3)/2} - 1 = 5 is prime.
a(5) = 2 since 3^1 + 3^{phi(4)/2} - 1 = 5 and 3^2 + 3^{phi(3)/2} - 1 are both prime.

Mathematica

f[n_, k_]:=3^k+3^(EulerPhi[n-k]/2)-1
a[n_]:=Sum[If[PrimeQ[f[n, k]], 1, 0], {k, 1, n-1}]
Table[a[n], {n, 1, 100}]

Crossrefs

Cf. A000010, A000040, A000244, A234309, A234310, A234337, A234344, A234346.

Sequence in context: A079086 A017839 A242294 * A328314 A286245 A279849

Adjacent sequences: A234344 A234345 A234346 * A234348 A234349 A234350

Keyword

nonn

Author

Zhi-Wei Sun, Dec 24 2013

Status

approved