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
Keywords
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.
Programs
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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
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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
Comments