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 A295512 The Euclid tree with root 1 encoded by semiprimes, read across levels. 4
 4, -6, 6, -21, 35, -35, 21, -10, 221, -77, 55, -55, 77, -221, 10, -33, 46513, -493, 377, -119, 187, -1333, 559, -559, 1333, -187, 119, -377, 493, -46513, 33, -14, 143, -209, 629, -14527, 2881, -1189, 533, -161, 391, -15229, 2449, -2263, 3139, -1073, 95, -95 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Euclid tree with root 1 is A295515 (sometimes called Calkin-Wilf tree). For a positive rational r we use the Schinzel-Sierpiński encoding r -> [p, q] as described in A295511 and encode r as sgn*p*q where sgn is -1 if r < 1, else +1. Apart from a(1) all terms are squarefree. REFERENCES E. Dijkstra, Selected Writings on Computing, Springer, 1982, p. 232. LINKS N. Calkin and H. S. Wilf, Recounting the rationals, Amer. Math. Monthly, 107 (No. 4, 2000), pp. 360-363. Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7. P. D. T. A. Elliott, The multiplicative group of rationals generated by the shifted primes. I., J. Reine Angew. Math. 463 (1995), 169-216. P. D. T. A. Elliott, The multiplicative group of rationals generated by the shifted primes. II. J. Reine Angew. Math. 519 (2000), 59-71. Peter Luschny, The Schinzel-Sierpiński conjecture and the Calkin-Wilf tree. A. Malter, D. Schleicher, D. Zagier, New looks at old number theory, Amer. Math. Monthly, 120(3), 2013, pp. 243-264. A. Schinzel and W. Sierpiński, Sur certaines hypothèses concernant les nombres premiers, Acta Arithmetica 4 (1958), 185-208; erratum 5 (1958) p. 259. EXAMPLE The tree starts:                      4             -6                 6        -21       35      -35       21     -10  221  -77  55  -55  77  -221  10 MAPLE EuclidTree := proc(n) local k, DijkstraFusc; DijkstraFusc := proc(m) option remember; local a, b, n; a := 1; b := 0; n := m; while n > 0 do if type(n, odd) then b := a+b else a := a+b fi; n := iquo(n, 2) od; b end: seq(DijkstraFusc(k)/DijkstraFusc(k+1), k=2^(n-1)..2^n-1) end: SchinzelSierpinski := proc(l) local a, b, r, p, q, sgn; a := numer(l); b := denom(l); q := 2; sgn := `if`(a < b, -1, 1); while q < 1000000000 do r := a*(q - 1); if r mod b = 0 then p := r/b + 1; if isprime(p) then return(sgn*p*q) fi fi; q := nextprime(q); od; print("Search limit reached!", a, b) end: Tree := level -> seq(SchinzelSierpinski(l), l=EuclidTree(level)): seq(Tree(n), n=1..6); CROSSREFS Cf. A294442, A295511, A295515. Sequence in context: A053320 A019090 A145692 * A064214 A019203 A082237 Adjacent sequences:  A295509 A295510 A295511 * A295513 A295514 A295515 KEYWORD sign,tabf AUTHOR Peter Luschny, Nov 23 2017 STATUS approved

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Last modified February 25 20:52 EST 2020. Contains 332258 sequences. (Running on oeis4.)