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

1,1

Comments

a(n) is the smallest prime such that there is no i < j < n with a(n) - a(j) = a(j) - a(i).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for non-averaging sequences

Example

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)

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 *)

Prog

(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

Crossrefs

Cf. A000040, A065825.

Sequence in context: A036958 A178317 A032024 * A277098 A096650 A111107

Adjacent sequences: A131738 A131739 A131740 * A131742 A131743 A131744

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 04 2007

Extensions

More terms from Ray Chandler, Oct 06 2007.

Status

approved