A136001 - OEIS

%I #16 Oct 20 2024 03:35:10

%S 11,23,29,47,59,71,79,83,89,107,131,139,149,167,179,181,191,197,199,

%T 223,227,233,239,251,263,269,307,311,347,349,359,373,379,383,389,419,

%U 431,439,443,449,461,467,479,491,503,509,563,569,571,587,593,599,607,643

%N Primes in A136000.

%H Amiram Eldar, <a href="/A136001/b136001.txt">Table of n, a(n) for n = 1..10000</a>

%H Dallas Symphony Association, <a href="https://www.dallassymphony.org/community-education/dso-kids/listen-watch/instruments/triangle/">Dsokids - Triangle instrument</a>.

%H Epsilones, <a href="https://web.archive.org/web/20160303215728/https://www.epsilones.com/imagenes/historia/pitagoras-musica.gif">Pythagoras - Music</a>.

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.

%e 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.

%p 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

%t 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 *)

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

%K nonn

%O 1,1

%A _Omar E. Pol_, Dec 10 2007

%E More terms from _R. J. Mathar_, Dec 12 2007

%E Extended by _Ray Chandler_, Dec 13 2008