A136001 Primes in A136000.

11, 23, 29, 47, 59, 71, 79, 83, 89, 107, 131, 139, 149, 167, 179, 181, 191, 197, 199, 223, 227, 233, 239, 251, 263, 269, 307, 311, 347, 349, 359, 373, 379, 383, 389, 419, 431, 439, 443, 449, 461, 467, 479, 491, 503, 509, 563, 569, 571, 587, 593, 599, 607, 643

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Dallas Symphony Association, Dsokids - Triangle instrument.

Epsilones, Pythagoras - Music.

Ron Knott, Pythagorean Triples and Online Calculators.

Example

a(1) = 11 because 11 is prime and {3,4,5} is a Pythagorean triple and 3+4+5 = 12 is the sum of a Pythagorean triple and 11+1 = 12, then we can write 3+4+5 = 11+1.

Maple

isprPer := proc(p) local dvs, m, n ; if p mod 2 = 1 then RETURN(false) ; fi ; dvs := p/2 ; for m in numtheory[divisors](dvs) do n := dvs/m-m ; if n > 0 and n < m then RETURN(true) ; fi ; od: RETURN(false) ; end: isA010814 := proc(n) local d; for d in numtheory[divisors](n) do if isprPer(n/d) then RETURN(true) ; fi ; od: RETURN(false) ; end: isA136000 := proc(n) isA010814(n+1) ; end: isA136001 := proc(n) isprime(n) and isA136000(n) ; end: for n from 2 to 600 do if isA136001(n) then printf("%d, ", n) ; fi: od: # R. J. Mathar, Dec 12 2007

Mathematica

q[n_] := PrimeQ[n] && Module[{d = Divisors[(n+1)/2]}, AnyTrue[Range[3, Length[d]], d[[#]] < 2 * d[[#-1]] &]]; Select[Range[650], q] (* Amiram Eldar, Oct 19 2024 *)

Crossrefs

Cf. A136000, A136003, A009096 (perimeters of Pythagorean triangles).

Sequence in context: A247228 A243461 A259560 * A158203 A161754 A038904

Adjacent sequences: A135998 A135999 A136000 * A136002 A136003 A136004

Keyword

nonn

Author

Omar E. Pol, Dec 10 2007

Extensions

More terms from R. J. Mathar, Dec 12 2007

Extended by Ray Chandler, Dec 13 2008

Status

approved