The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A155114 Number of ways to express n as the sum of an odd prime, a positive Fibonacci number and twice a positive Fibonacci number. 8
 0, 0, 0, 0, 0, 1, 1, 3, 2, 6, 3, 7, 3, 8, 5, 8, 6, 10, 5, 11, 6, 13, 7, 13, 7, 14, 5, 14, 7, 15, 8, 14, 4, 18, 8, 17, 7, 15, 5, 15, 11, 16, 8, 15, 7, 17, 12, 19, 10, 20, 10, 17, 10, 17, 13, 15, 11, 18, 8, 20, 10, 17, 9, 18, 11, 21, 11, 21, 7, 20, 11, 18, 11, 22, 9, 25, 11, 24, 13, 19, 14, 20, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Motivated by his conjecture related to A154257, on Dec 26 2008, Zhi-Wei Sun conjectured that a(n)>0 for n=6,7,... On Jan 15 2009, D. S. McNeil verified this up to 10^12 and found no counterexamples. See the sequence A154536 for another conjecture of this sort. Sun also conjectured that any integer n>7 can be written as the sum of an odd prime, twice a positive Fibonacci number and the square of a positive Fibonacci number; this has been verified up to 2*10^8. REFERENCES R. Crocker, On a sum of a prime and two powers of two, Pacific J. Math. 36(1971), 103-107. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..100000 D. S. McNeil, Various and sundry (a report on Sun's conjectures) Zhi-Wei Sun, A promising conjecture: n=p+F_s+F_t Zhi-Wei Sun, A summary concerning my conjecture n=p+F_s+F_t (II) Terence Tao, A remark on primality testing and decimal expansions, Journal of the Australian Mathematical Society 91:3 (2011), pp. 405-413. K. J. Wu and Z. W. Sun, Covers of the integers with odd moduli and their applications to the forms x^m-2^n and x^2-F_{3n}/2, Math. Comp. 78 (2009) 1853-1866. arXiv:math.NT/0702382. FORMULA a(n) = |{: p+F_s+2F_t=n with p an odd prime and s,t>1}|. EXAMPLE For n=10 the a(10)=6 solutions are 3 + F_4 + 2F_3, 3 + F_5 + 2F_2, 3 + F_2 + 2F_4, 5 + F_2 + 2F_3, 5 + F_4 + 2F_2, 7 + F_2 + 2F_2. MATHEMATICA PQ[m_]:=m>2&&PrimeQ[m] RN[n_]:=Sum[If[PQ[n-2*Fibonacci[x]-Fibonacci[y]], 1, 0], {x, 2, 2*Log[2, Max[2, n/2]]}, {y, 2, 2*Log[2, Max[2, n-2*Fibonacci[x]]]}] Do[Print[n, " ", RN[n]]; Continue, {n, 1, 100000}] CROSSREFS Cf. A000040, A000045, A154257, A154258, A154263, A154285, A154290, A154417, A154536, A154404, A154940, A156695. Sequence in context: A322907 A071018 A144559 * A038572 A334667 A245676 Adjacent sequences:  A155111 A155112 A155113 * A155115 A155116 A155117 KEYWORD nice,nonn AUTHOR Zhi-Wei Sun, Jan 20 2009 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 November 23 21:51 EST 2020. Contains 338603 sequences. (Running on oeis4.)