The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A235919 a(n) = |{0 < k < n - 2: p = prime(k) + phi(n-k)/2, prime(p) - p + 1 and (p^2 - 1)/4 - prime(p) are all prime}|, where phi(.) is Euler's totient function. 2
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 1, 2, 3, 1, 0, 3, 3, 2, 1, 2, 1, 3, 2, 4, 2, 1, 6, 2, 6, 2, 3, 2, 3, 6, 2, 1, 7, 2, 5, 4, 3, 4, 3, 6, 4, 5, 4, 2, 1, 2, 8, 2, 4, 5, 5, 6, 4, 5, 4, 6, 3, 3, 5, 6, 5, 3, 4, 8, 2, 3, 7, 7, 8, 5, 5, 3, 3, 7, 9, 3, 8, 2, 4, 4, 4, 9, 2, 5, 8, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,18 COMMENTS Conjecture: a(n) > 0 for all n > 24. This implies that there are infinitely many primes p with prime(p) - p + 1 and (p^2 - 1)/4 - prime(p) both prime. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(30) = 1 since prime(6) + phi(24)/2 = 13 + 4 = 17, prime(17) - 16 = 59 - 16 = 43 and (17^2 - 1)/4 - prime(17) = 72 - 59 = 13 are all prime. a(35) = 1 since prime(19) + phi(16)/2 = 67 + 4 = 71, prime(71) - 70 = 353 - 70 = 283 and (71^2 - 1)/4 - prime(71) = 1260 - 353 = 907 are all prime. MATHEMATICA PQ[n_]:=PQ[n]=n>0&&PrimeQ[n] p[n_]:=p[n]=PrimeQ[n]&&PrimeQ[Prime[n]-n+1]&&PQ[(n^2-1)/4-Prime[n]] f[n_, k_]:=f[n, k]=Prime[k]+EulerPhi[n-k]/2 a[n_]:=a[n]=Sum[If[p[f[n, k]], 1, 0], {k, 1, n-3}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000010, A000040, A234695, A235917. Sequence in context: A231188 A249695 A136748 * A229654 A306288 A272188 Adjacent sequences: A235916 A235917 A235918 * A235920 A235921 A235922 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jan 17 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 29 03:54 EDT 2023. Contains 365750 sequences. (Running on oeis4.)