login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085401 a(0) = 1; a(n+1) is the smallest positive number (of at most two) such that abs(a(n) - a(n+1)) is the smallest prime not occurring earlier as difference of successive terms and a(n) + a(n+1) is composite. 2

%I

%S 1,3,6,19,14,7,18,37,20,43,14,51,82,41,84,37,96,149,88,155,226,299,

%T 220,137,48,155,58,159,56,165,52,179,310,173,34,183,32,189,26,193,20,

%U 199,18,217,26,219,416,205,428,201,434,205,444,193,434,177,446,183,454,731

%N a(0) = 1; a(n+1) is the smallest positive number (of at most two) such that abs(a(n) - a(n+1)) is the smallest prime not occurring earlier as difference of successive terms and a(n) + a(n+1) is composite.

%C There are numbers which occur more than once, e.g. a(6) = a(42) = 18, a(8) = a(40) = 20.

%C Problem: Does every positive integer eventually occur?

%e a(4) = 14; the smallest prime not occurring earlier as difference of successive terms is 7; there are two numbers x such that abs(14 - x) = 7 and 14 + x is composite, namely x = 7 and x = 21. The smaller of these numbers is 7, so a(5) = 7.

%e a(11) = 51; the smallest prime not occurring earlier as difference of successive terms is 31; there are two numbers x such that abs(51 - x) = 31, namely x = 20 and x = 82 and 51 + 20 = 71 is not composite while 51 + 82 = 133 is composite;

%e hence a(12) = 82.

%o (PARI) {in(n,v)=local(j,s,b); j=1; s=matsize(v)[2]; b=1; while(b&&j<=s,if(n==v[j],b=0,j++)); !b}

%o {print1(a=1,","); v=[]; for(n=1,60,p=2; t=1; while(t>0,if(in(p,v),p=nextprime(p+1),if(p<a&&!isprime(2*a-p),t=0; b=a-p,if(!isprime(2*a+p),t=0; b=a+p,p=nextprime(p+1))))); v=concat(v,p); print1(a=b,","))}

%Y Cf. A085061, A085402.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jun 28 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 02:24 EST 2014. Contains 250286 sequences.