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!)
 A308411 Number of ways to write n as 2^i*3^j + A008347(k), where i, j and k > 0 are nonnegative integers. 6
 0, 1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 3, 5, 5, 4, 5, 5, 3, 6, 7, 6, 6, 5, 6, 7, 4, 5, 8, 6, 8, 7, 5, 5, 8, 8, 6, 7, 5, 7, 8, 7, 6, 6, 6, 8, 6, 5, 8, 6, 7, 7, 5, 8, 7, 8, 10, 9, 9, 6, 7, 8, 8, 6, 7, 10, 8, 8, 6, 9, 6, 7, 9, 8, 7, 7, 8, 9, 4, 8, 11, 10, 6, 9, 7, 11, 8, 8, 10, 9, 6, 4, 7, 10, 7, 7, 3, 11, 9, 10, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Conjecture: a(n) > 0 for all n > 1. We have verified this for all n = 2..10^6. Qing-Hu Hou at Tianjin University extended the verification to 2*10^7. Then I used Hou's program to verify a(n) > 0 for n up to 10^9. - Zhi-Wei Sun, May 28 2019 Conjecture verified for n up to 10^10. - Giovanni Resta, May 28 2019 LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, On functions taking only prime values, J. Number Theory 133(2013), no.8, 2794-2812. EXAMPLE a(2) = 1 with 2 = 2^0*3^0 + A008347(2). a(3) = 2 with 3 = 2^0*3^0 + A008347(1) = 2^1*3^0 + A008347(2). MATHEMATICA f[n_]:=f[n]=FactorInteger[n]; FQ[n_]:=FQ[n]=n>0&&Part[f[n], Length[f[n]]][[1]]<4; s[0]=0; s[n_]:=s[n]=Prime[n]-s[n-1]; tab={}; Do[r=0; Do[If[FQ[n-s[k]], r=r+1], {k, 1, 2n-1}]; tab=Append[tab, r], {n, 1, 100}]; Print[tab] CROSSREFS Cf. A000079, A000244, A008347, A308403, A316141. Sequence in context: A195850 A253593 A174901 * A087848 A087844 A287635 Adjacent sequences:  A308408 A308409 A308410 * A308412 A308413 A308414 KEYWORD nonn AUTHOR Zhi-Wei Sun, May 25 2019 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 27 12:23 EST 2020. Contains 338683 sequences. (Running on oeis4.)