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

Author

Omar E. Pol, Dec 10 2007

Keywords

• nonn

Examples

			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.
		

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.

Crossrefs

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

Programs

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 *)

Extensions

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

Extended by Ray Chandler, Dec 13 2008