The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A225889 Least prime p_m such that n = p_m-p_{m-1}+...+(-1)^(m-k)*p_k for some 0
 3, 5, 7, 5, 7, 11, 13, 11, 11, 17, 19, 17, 17, 23, 17, 23, 23, 31, 23, 41, 23, 41, 31, 47, 29, 47, 37, 59, 41, 59, 37, 59, 43, 67, 37, 67, 43, 67, 43, 73, 61, 83, 53, 83, 47, 101, 61, 97, 53, 97, 59, 97, 59, 103, 61, 109, 67, 127, 67, 131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS By a conjecture of the author, a(n) <= 2*n+2.2*sqrt(n), and moreover a(n) <= n+4.6*sqrt(n) if n is odd. Clearly a(n)>n. We guess that a(2n)/(2n) --> 2 as n tends to the infinity. Note that this sequence is different from A222579 which involves a stronger conjecture of the author. Zhi-Wei Sun also conjectured that any positive even integer m can be written in the form p_n-p_{n-1}+...+(-1)^{n-k}*p_k with k < n and 2m-3.6*sqrt(m+1) < p_n < 2m+2.2*sqrt(m). 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(7) = 13 since 7 = 13-11+7-5+3. a(20) = 41 since 20 = 41-37+31-29+23-19+17-13+11-7+5-3. MATHEMATICA s[0_]:=0 s[n_]:=s[n]=Prime[n]-s[n-1] Do[Do[If[s[j]-(-1)^(j-i)*s[i]==m, Print[m, " ", Prime[j]]; Goto[aa]], {j, PrimePi[m]+1, PrimePi[2m+2.2Sqrt[m]]}, {i, 0, j-2}]; Print[m, " ", counterexample]; Label[aa]; Continue, {m, 1, 100}] CROSSREFS Cf. A000040, A222579. Sequence in context: A141710 A279399 A321784 * A070647 A070949 A222579 Adjacent sequences:  A225886 A225887 A225888 * A225890 A225891 A225892 KEYWORD nonn AUTHOR Zhi-Wei Sun, May 19 2013 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 July 31 14:49 EDT 2021. Contains 346374 sequences. (Running on oeis4.)