This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A236389 a(n) = |{0 < k < n: m = phi(k)/2 + phi(n-k)/12 is an integer with 2^m*p(m) + 1 prime}|, where p(.) is the partition function (A000041). 2
 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1, 0, 4, 3, 2, 0, 2, 3, 2, 2, 4, 2, 2, 1, 3, 2, 1, 2, 3, 3, 5, 3, 3, 4, 2, 8, 3, 2, 4, 4, 2, 4, 3, 5, 3, 5, 5, 3, 7, 3, 6, 6, 6, 4, 4, 2, 9, 3, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,38 COMMENTS Conjecture: a(n) > 0 for all n > 56. We have verified this for n up to 33000. The conjecture implies that there are infinitely many positive integers m with 2^m*p(m) + 1 prime. See A236390 for a list of such numbers m. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(10) = 1 since phi(1)/2 + phi(9)/12 = 1/2 + 6/12 = 1 with 2^1*p(1) + 1 = 2 + 1 = 3 prime. a(30) = 1 since phi(17)/2 + phi(13)/12 = 8 + 1 = 9 with 2^9*p(9) + 1 = 512*30 + 1 = 15361 prime. a(8261) = 1 since phi(395)/2 + phi(8261-395)/12 = 156 + 198 = 354 with 2^(354)*p(354) + 1 = 2^(354)*363117512048110005 + 1 prime. MATHEMATICA q[n_]:=IntegerQ[n]&&PrimeQ[2^n*PartitionsP[n]+1] f[n_, k_]:=EulerPhi[k]/2+EulerPhi[n-k]/12 a[n_]:=Sum[If[q[f[n, k]], 1, 0], {k, 1, n-1}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000010, A000040, A000041, A000079, A236390. Sequence in context: A159459 A304095 A276675 * A143078 A106405 A228601 Adjacent sequences:  A236386 A236387 A236388 * A236390 A236391 A236392 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jan 24 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.

Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)