A105822 -id:A105822 - cp's OEIS frontend

A104663 Position of n in A105822.

1, 2, 3, 6, 4, 11, 8, 5, 26, 9, 12, 7, 15, 17, 33, 43, 10, 25, 16, 19, 13, 32, 39, 21, 61, 175, 22, 20, 57, 37, 95, 14, 18, 50, 27, 40, 34, 110, 29, 24, 171, 23, 64, 28, 46, 203, 45, 31, 137, 91, 134, 35, 58, 30, 90, 54, 69, 106, 38, 73, 360, 296, 67, 88, 48, 70, 526, 109, 124

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Is A105822 a permutation of the positive integers?

Ivan Neretin, Table of n, a(n) for n = 1..1000

Cf. A105822.

N:= 1000: # to go up to the first entry missing in A105822(1 .. N)
A:= 'A':
a[1]:= 1: a[2]:= 2:
A[1]:= 1: A[2]:= 2:
for n from 3 to N do
  ds:= map(t -> rhs(op(t)), [msolve(x^2=a[n-1]^2, 4*a[n-2])]);
  xmin:= infinity;
  for d in ds do
    found:= false;
    for y from floor((a[n-1]-d)/(4*a[n-2]))+1 do
      xy:= 4*a[n-2]*y + d;
      cand:= (xy^2 - a[n-1]^2)/(4*a[n-2]);
      if cand >= xmin then found:= false; break fi;
      if not assigned(A[cand]) then found:= true; break fi;
    od:
    if found then xmin:= cand;  fi;
  od:
  a[n]:= xmin;
  A[xmin]:= n;
od:
M:= min(select(t -> not assigned(A[t]), [$1..N+1])):
seq(A[i],i=1..M-1); # Robert Israel, May 11 2015

Definition corrected by N. J. A. Sloane, Aug 29 2008

A105823 Perfect squares in A105822.

Original entry on oeis.org

16, 49, 121, 144, 400, 256, 529, 576, 529, 784, 625, 1849, 2116, 2601, 1089, 2704, 2209, 4096, 2704, 3600, 4761, 6084, 4624, 1764, 2601, 2809, 7396, 11025, 10404, 7056, 3364, 3481, 4489, 15876, 14161, 21904, 6241, 9025, 10404, 19881, 11236

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Cf. A105822.

a(n)=A105822(n+1)^2+4*A105822(n)*A105822(n+2)

A104664 Records in A105822.

Original entry on oeis.org

1, 2, 3, 5, 8, 12, 17, 21, 32, 33, 42, 44, 54, 89, 99, 157, 222, 236, 258, 327, 345, 371, 470, 495, 606, 634, 866, 891, 1219, 1383, 1540, 1626, 1660, 1878, 1989, 2064, 2758, 3534, 3954, 4053, 4113, 4468, 4618, 4783, 4862, 5134, 6394, 7176, 7480, 11649

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Is A105822 a permutation of positive integers?

Cf. A105822.

A104665 Positions of records in A105822.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 10, 13, 14, 18, 23, 28, 30, 36, 41, 49, 53, 77, 85, 102, 114, 141, 151, 163, 174, 182, 188, 244, 263, 311, 419, 434, 468, 477, 478, 655, 656, 739, 768, 890, 1002, 1027, 1099, 1118, 1166, 1365, 1397, 1440, 1574, 1575

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Is A105822 a permutation of positive integers?

Cf. A105822.

A105836 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=2, a(2)=3.

Original entry on oeis.org

2, 3, 5, 8, 4, 12, 7, 10, 17, 6, 11, 21, 32, 13, 19, 14, 33, 20, 28, 24, 27, 42, 40, 18, 1, 39, 82, 72, 154, 43, 35, 78, 56, 22, 9, 31, 70, 69, 52, 25, 48, 73, 46, 119, 57, 26, 15, 36, 51, 50, 101, 60, 41, 54, 95, 61, 16, 45, 76, 121, 62, 59, 130, 141, 81, 222, 63, 87, 30, 117

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A105822, A105828-A105835.

A105828 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=3.

Original entry on oeis.org

1, 3, 4, 7, 2, 5, 12, 9, 21, 8, 13, 6, 19, 11, 30, 41, 15, 26, 24, 50, 14, 36, 18, 10, 28, 38, 66, 20, 16, 48, 45, 93, 72, 165, 63, 102, 96, 198, 105, 23, 62, 85, 58, 27, 31, 46, 32, 78, 47, 43, 90, 117, 22, 95, 53, 42, 128, 40, 25, 65, 68, 124, 79, 129, 208, 100, 108, 184, 64

Offset: 1

Zak Seidov, Apr 22 2005

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A105822, A105829-A105836.

A105835 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=10.

Original entry on oeis.org

1, 10, 11, 6, 5, 4, 9, 13, 22, 8, 14, 15, 26, 21, 17, 30, 47, 19, 28, 20, 33, 27, 60, 7, 2, 24, 56, 34, 12, 46, 36, 82, 50, 32, 18, 45, 38, 35, 3, 54, 57, 25, 42, 16, 58, 63, 106, 40, 66, 43, 23, 126, 72, 104, 70, 61, 39, 100, 51, 49, 156, 160, 31, 129, 130, 144, 162, 81, 68

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A105822, A105828-A105836.

A105829 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=4.

Original entry on oeis.org

1, 4, 5, 6, 8, 14, 9, 18, 7, 11, 30, 41, 15, 26, 21, 17, 38, 39, 27, 12, 20, 13, 33, 46, 19, 2, 72, 74, 23, 51, 54, 96, 24, 36, 60, 56, 32, 78, 47, 10, 37, 65, 102, 167, 67, 100, 68, 59, 105, 164, 45, 119, 48, 71, 29, 42, 135, 132, 3, 129, 270, 351, 66, 40, 64, 90, 61, 53, 114

Offset: 1

Zak Seidov, Apr 22 2005

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A105822, A105828-A105836.

A105834 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=9.

Original entry on oeis.org

1, 9, 10, 16, 8, 3, 5, 2, 7, 4, 11, 15, 14, 29, 18, 47, 21, 26, 32, 40, 12, 28, 17, 6, 23, 13, 36, 49, 46, 95, 50, 45, 35, 80, 75, 155, 22, 69, 76, 33, 43, 20, 63, 68, 91, 27, 64, 51, 115, 44, 71, 34, 37, 62, 24, 38, 25, 48, 73, 70, 143, 60, 83, 19, 102, 72, 30, 42, 144, 96, 65

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A105822, A105828-A105836.

A105830 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=5.

Original entry on oeis.org

1, 5, 6, 8, 14, 4, 10, 24, 18, 15, 3, 12, 36, 21, 2, 19, 33, 52, 28, 27, 55, 78, 16, 62, 35, 87, 54, 141, 25, 46, 71, 42, 29, 13, 90, 7, 26, 45, 50, 80, 40, 75, 115, 58, 57, 43, 44, 84, 53, 22, 31, 60, 91, 37, 20, 17, 63, 110, 32, 96, 56, 132, 108, 135, 138, 61, 65, 114, 143, 100

Offset: 1

Zak Seidov, Apr 22 2005

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A105822, A105828-A105836.

cp's OEIS Frontend

A104663 Position of n in A105822.

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A105823 Perfect squares in A105822.

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A104664 Records in A105822.

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A104665 Positions of records in A105822.

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A105836 For n>2, a(n) not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=2, a(2)=3.

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A105828 For n>2, a(n) not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=3.

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A105835 For n>2, a(n) not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=10.

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A105829 For n>2, a(n) not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=4.

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A105834 For n>2, a(n) not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=9.

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A105830 For n>2, a(n) not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=5.

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A105836 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=2, a(2)=3.

A105828 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=3.

A105835 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=10.

A105829 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=4.

A105834 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=9.

A105830 For n>2, a(n) not appeared previously is such that a(n-1)^2+4a(n-2)a(n) is a minimal square, a(1)=1, a(2)=5.