

A234347


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


14



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
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OFFSET

1,5


COMMENTS

Conjecture: a(n) > 0 for all n > 3.
See also the conjecture in A234337.


LINKS

ZhiWei 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[nk]/2)1
a[n_]:=Sum[If[PrimeQ[f[n, k]], 1, 0], {k, 1, n1}]
Table[a[n], {n, 1, 100}]


CROSSREFS

Cf. A000010, A000040, A000244, A234309, A234310, A234337, A234344, A234346.
Sequence in context: A079086 A017839 A242294 * A286245 A279849 A106826
Adjacent sequences: A234344 A234345 A234346 * A234348 A234349 A234350


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Dec 24 2013


STATUS

approved



