|
Search: id:A131741
|
|
|
| A131741 |
|
a(n) is least prime (not already in list) such that no 3-term subset forms an arithmetic progression. |
|
+0
3
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
a(n) is the smallest prime such that there is no i < j < n with a(n) - a(j) = a(j) - a(i).
|
|
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 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 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]
|
|
CROSSREFS
|
Cf. A000040, A065825.
Sequence in context: A133783 A036958 A032024 this_sequence A096650 A111107 A129201
Adjacent sequences: A131738 A131739 A131740 this_sequence A131742 A131743 A131744
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 04 2007
|
|
EXTENSIONS
|
More terms and program from Ray Chandler (rayjchandler(AT)sbcglobal.net).
|
|
|
Search completed in 0.002 seconds
|
