login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236470 a(n) = |{0 < k < n: p = prime(k) + phi(n-k), p + 2 and prime(p) + 2 are all prime}}, where phi(.) is Euler's totient function. 6
0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 0, 1, 1, 0, 3, 0, 1, 0, 1, 3, 0, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

COMMENTS

Conjecture: a(n) > 0 for all n > 948.

We have verified this for n up to 50000.

The conjecture implies that there are infinitely many primes p with p + 2 and prime(p) + 2 both prime. See A236458 for such primes p.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(12) = 1 since prime(5) + phi(7) = 11 + 6 = 17, 17 + 2 = 19 and prime(17) + 2 = 59 + 2 = 61 are all prime.

a(97) = 1 since prime(7) + phi(90) = 17 + 24 = 41, 41 + 2 = 43 and prime(41) + 2 = 179 + 2 = 181 are all prime.

MATHEMATICA

p[n_]:=PrimeQ[n]&&PrimeQ[n+2]&&PrimeQ[Prime[n]+2]

f[n_, k_]:=Prime[k]+EulerPhi[n-k]

a[n_]:=Sum[If[p[f[n, k]], 1, 0], {k, 1, n-1}]

Table[a[n], {n, 1, 100}]

CROSSREFS

Cf. A000010, A000040, A001359, A006512, A236097, A236456, A236458, A236468.

Sequence in context: A218854 A172303 A064391 * A206589 A086011 A124760

Adjacent sequences:  A236467 A236468 A236469 * A236471 A236472 A236473

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 26 2014

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 29 04:52 EDT 2021. Contains 346340 sequences. (Running on oeis4.)