|
%I #7 Aug 25 2014 11:40:47
%S 1,3,6,19,14,21,4,23,34,57,86,117,158,121,164,211,264,205,266,199,270,
%T 353,426,505,594,691,590,487,594,485,598,725,856,993,1132,1281,1124,
%U 973,1136,1303,1476,1655,1474,1665,1858,2055,2254,2465,2242,2469,2240,2473
%N a(0) = 1; a(n+1) is the largest 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 Conjecture 1: a(n+5) > a(n).
%C Conjecture 2: There are no numbers which occur more than once.
%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 larger of these numbers is 21, so a(5) = 21.
%e a(5) = 21; the smallest primes not occurring earlier as difference of successive terms are 11 and 17; there are two numbers x such that abs(21 - x) = 11, namely x = 10 and x = 32, but neither 21 + 10 = 31 nor 21 + 32 = 53 is composite;
%e there are two numbers x such that abs(21 - x) = 17, namely x = 4 and x = 38 and 21 + 38 = 59 is not composite while 21 + 4 = 25 is composite; hence a(6) = 4.
%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=1,51,p=2; t=1; while(t>0,if(in(p,v),p=nextprime(p+1),if(!isprime(2*a+p),t=0; b=a+p,if(p<a&&!isprime(2*a-p),t=0; b=a-p,p=nextprime(p+1))))); v=concat(v,p); print1(a=b,","))}
%Y Cf. A085400, A085401.
%K nonn
%O 0,2
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 27 2003
%E Edited, corrected and extended by _Klaus Brockhaus_, Jun 28 2003
|
