

A131741


a(n) is least prime (not already in list) such that no 3term subset forms an arithmetic progression.


4



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
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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 nonaveraging 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



