|
Search: id:A159296
|
|
|
| A159296 |
|
a(n) is the smaller number in the pair (l,m) which minimizes the primes of the form l^2+m^2 under the constraint l+m=2n+1. |
|
+0
2
|
|
| 1, 2, 2, 4, 5, 5, 7, 7, 9, 8, 10, 12, 10, 14, 11, 14, 17, 15, 19, 18, 20, 22, 22, 24, 25, 25, 23, 26, 29, 30, 29, 32, 30, 34, 35, 34, 34, 37, 39, 31, 40, 42, 41, 40, 43, 44, 47, 45, 40, 50, 50, 47, 51, 52, 53, 55, 54, 56, 55, 60, 59, 61, 62, 55, 65, 65, 64, 66, 69, 70, 64, 72, 67, 72, 65
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
1) It is known that sequence is infinite.
2) l and m with odd sum l+m are necessarily relative prime if l^2+m^2 is prime.
3) The "singular" case m=l=1, l+m=2 (even) with 1^2+1^2=2 is skipped. It would define a(0)=1.
4) a(n) <= n
It has not been proved that a(n) exists for all n. See A036468. [From T. D. Noe (noe(AT)sspectra.com), Apr 22 2009]
|
|
EXAMPLE
|
n=1: 1^2+2^2=5; a(1)=1.
n=2: 2^2+3^2=13 < 1^2+4^2=17; a(2)=2.
n=3: 2^2+5^2=29 < 1^2+6^2=37. 3^2+4^2=5^2 not prime; a(3)=2.
n=27: 23^2+32^2=1553 < 1597, 1657, 1693, 1733, 1777, 1877, 1933, 1993, 2273, 2437, 2617, 2713, 2917, a(27)=23.
|
|
MAPLE
|
A159296 := proc(n) local a, pmin, l, m ; a := 0 ; pmin := 2*(2*n+1)^2 ; for l from 1 to n do m := 2*n+1-l ; if isprime(m^2+l^2) then if m^2+l^2 < pmin then pmin := m^2+l^2 ; a := l ; fi; fi; od: RETURN(a) ; end: seq(A159296(n), n=1..80) ; # R. J. Mathar, Apr 18 2009
|
|
CROSSREFS
|
Cf. A145354, A157884.
Sequence in context: A115216 A122543 A118003 this_sequence A035632 A114701 A049269
Adjacent sequences: A159293 A159294 A159295 this_sequence A159297 A159298 A159299
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 09 2009
|
|
EXTENSIONS
|
Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 18 2009
|
|
|
Search completed in 0.002 seconds
|
