A131741 a(n) is least prime (not already in list) such that no 3-term subset forms an arithmetic progression.
2, 3, 5, 11, 13, 29, 31, 37, 41, 67, 73, 83, 89, 101, 107, 127, 139, 157, 179, 193, 227, 233, 263, 271, 281, 307, 331, 337, 379, 389, 397, 401, 409, 431, 433, 467, 491, 499, 509, 563, 571, 613, 641, 647, 743, 769, 809, 823, 883, 887, 907, 937, 983, 1009, 1021
Offset: 1
Examples
Table showing derivation of first 10 values. n a(n) comment 1 2 2 3 3 5 4 11 a(4) can't be 7 because (3,5,7) is in arithmetic progression. 5 13 6 29 a(6) can't be 17 because (5,11,17); can't be 19 because (3,11,19); can't be 23 because (3,13,23) 7 31 8 37 9 41 10 67 a(10) not 43 as (31,37,43); not 47 as (11,29,47); not 53 as (29,41,53); not 59 as (13,31,59); not 61 as (13,37,61)
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for non-averaging sequences
Programs
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Mathematica
f[l_List] := Block[{c, f = 0}, c = If[l == {}, 0, l[[ -1]]]; While[f == 0, c = NextPrime[c]; If[Intersection[l, l - (c - l)] == {}, f = 1]; ]; Append[l, c] ]; Nest[f, {}, 100] (* Ray Chandler, Oct 06 2007 *) -
PARI
nxt(v)=my(t); forprime(p=v[#v]+1,,forstep(i=#v,3,-1,t=2*v[i]-p; if(t<3, if(i==#v,break,next)); if(setsearch(v,t),next(2))); return(p)) list(n)=my(v=[2]);for(k=2,n,v=concat(v,nxt(v))); v \\ Charles R Greathouse IV, Jan 30 2014
Extensions
More terms from Ray Chandler, Oct 06 2007.
Comments