This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A234359 a(n) = |{2 < k < n-2: 5^{phi(k)} + 5^{phi(n-k)/2} - 1 is prime}|, where phi(.) is Euler's totient function. 10
 0, 0, 0, 0, 0, 1, 2, 1, 2, 4, 2, 4, 4, 3, 4, 3, 6, 5, 4, 6, 7, 8, 6, 7, 11, 7, 10, 9, 9, 7, 10, 11, 8, 7, 11, 10, 9, 6, 11, 15, 4, 14, 5, 14, 11, 13, 9, 13, 6, 12, 10, 12, 11, 10, 10, 13, 9, 7, 11, 7, 11, 4, 11, 9, 10, 6, 11, 8, 4, 10, 12, 13, 9, 7, 9, 6, 12, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Conjecture: For any integer a > 1, there is a positive integer N(a) such that if n > N(a) then a^{phi(k)} + a^{phi(n-k)/2} - 1 is prime for some 2 < k < n-2. Moreover, we may take N(2) = N(3) = ... = N(6) = N(8) = 5 and N(7) = 17. Clearly, this conjecture implies that for each  a = 2, 3, ... there are infinitely many primes of the form a^{2*k} + a^m - 1, where k and m are positive integers. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..2500 EXAMPLE a(6) = 1 since 5^{phi(3)} + 5^{phi(3)/2} - 1 = 29 is prime. a(11) = 2 since 5^{phi(4)} + 5^{phi(7)/2} - 1 = 149 and 5^{phi(7)} + 5^{phi(4)/2} - 1 = 15629 are both prime. MATHEMATICA f[n_, k_]:=5^(EulerPhi[k])+5^(EulerPhi[n-k]/2)-1 a[n_]:=Sum[If[PrimeQ[f[n, k]], 1, 0], {k, 3, n-3}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000010, A000040, A000351, A234309, A234310, A234337, A234344, A234346, A234347 Sequence in context: A121339 A307236 A324382 * A099500 A120253 A307018 Adjacent sequences:  A234356 A234357 A234358 * A234360 A234361 A234362 KEYWORD nonn AUTHOR Zhi-Wei Sun, Dec 24 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 20 20:50 EDT 2019. Contains 326155 sequences. (Running on oeis4.)