|
| |
|
|
A094550
|
|
Numbers n such that there are integers a < b with a+(a+1)+...+(n-1) = (n+1)+(n+2)+...+b.
|
|
8
|
|
|
|
4, 6, 9, 11, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 59, 61, 64, 66, 68, 69, 70, 71, 72, 74, 76, 77, 79, 81, 82, 83, 84, 86, 87, 89, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Liljestrom shows that n is in this sequence if and only if 4n^2+1 is composite.
For n > 1, A047209 is a subset of this sequence [ 4*n^2+1 is divisible by 5 if n is (1 or 4) mod 5].
A092464 is a subset of this sequence [4*n^2+1 is divisible by 13 if n is (4 or 9) mod 13].
The above are for divisibility by 5, 13; notation (1,4,5), (4,9,13). Divisibility by p for a and p-a; notation (a,p-a,p). These are the next tuples: (2,15,17), (6,23,29), (3,34,37), (16,25,41), ... . The corresponding sequences are a subset of this sequence [ 2,15,19,32,36,49,... for (2,15,17) ]. These sequences have no entries in the OEIS yet. For any prime of the form 4*k+1 there is exactly one of these tuples/sequences [solution to 4*a^2+1=0 (mod p)].
For n>1, A000290 (squares) is a subset of this sequence (4,9,16,25,...) [ 4*(m^2)^2+1 is divisible by m^2+(m+1)^2, tuple (m^2, (m+1)^2, m^2+(m+1)^2) ].
(End)
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
6 is in this sequence because 1+2+3+4+5 = 7+8.
|
|
|
MATHEMATICA
|
lst={}; Do[i1=n-1; i2=n+1; s1=i1; s2=i2; While[i1>1 && s1!=s2, If[s1<s2, i1--; s1=s1+i1, i2++; s2=s2+i2]]; If[s1==s2, AppendTo[lst, n]], {n, 2, 140}];
lst (* end of program *)
Select[Range[1000], !PrimeQ[4#^2+1]&] (* T. D. Noe, Nov 12 2010 *)
|
|
|
PROG
|
(Magma) [n: n in [1..100] |not IsPrime(4*n^2 + 1)]; // Vincenzo Librandi, Sep 27 2012 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
