A026166 -id:A026166 - cp's OEIS frontend

A026200 a(n) = (s(n) + 2)/3, where s(n) is the n-th number congruent to 1 mod 3 in A026166.

1, 2, 4, 6, 3, 8, 10, 12, 5, 14, 16, 18, 7, 20, 22, 24, 9, 26, 28, 30, 11, 32, 34, 36, 13, 38, 40, 42, 15, 44, 46, 48, 17, 50, 52, 54, 19, 56, 58, 60, 21, 62, 64, 66, 23, 68, 70, 72, 25, 74, 76, 78, 27, 80, 82, 84, 29, 86, 88, 90, 31, 92, 94

Offset: 1

Clark Kimberling

nonn

			Conjectures from _Colin Barker_, Oct 14 2019: (Start)
G.f.: x*(1 + 2*x + 4*x^2 + 6*x^3 + x^4 + 4*x^5 + 2*x^6) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).
a(n) = 2*a(n-4) - a(n-8) for n>8.
(End)

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Cf. A026166.

\\ here S is A026166 as vector.
S(n)={my(a=vector(n)); a[1]=1; for(i=1, 2*n-1, my(h=(i-1)\2); if(!a[i-h], a[i-h]=i, if(i+h<=n, a[i+h]=i))); a}
{[(k + 2)/3 | k<-S(500), k%3==1]} \\ Andrew Howroyd, Oct 15 2019

Title corrected by Sean A. Irvine, Sep 20 2019

A026167 a(n) is the position of n in A026166.

Original entry on oeis.org

1, 2, 4, 3, 7, 8, 10, 5, 13, 6, 16, 17, 19, 20, 22, 9, 25, 26, 28, 11, 31, 12, 34, 35, 37, 14, 40, 15, 43, 44, 46, 47, 49, 18, 52, 53, 55, 56, 58, 21, 61, 62, 64, 23, 67, 24, 70, 71, 73, 74, 76, 27, 79, 80, 82, 29, 85, 30, 88, 89, 91, 32, 94

Offset: 1

Clark Kimberling

nonn

This permutation of the positive integers is the inverse of A026166. - Clark Kimberling, Oct 20 2019

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A026166.

a[1] = 1; z = 3000;
Do[{L, R} = {n - #, n + #} &[Floor[(n - 1)/2]];
  If[! Head[a[L]] === Integer, a[L] = n, a[R] = n], {n, 2, z}];
a026166 = Most[Last[
   Last[Reap[NestWhile[# + 1 &, 1, Head[Sow[a[#]]] === Integer &]]]]]; (* A026166 *)
Flatten[Table[Position[a026166, n], {n, 1, 1000}]]  (* A026167 *)
(* Peter J. C. Moses, Oct 20 2019 *)

A026202 a(n) = (1/4)*s(n), where s(n) is the n-th multiple of 4 in A026166.

Original entry on oeis.org

1, 2, 4, 5, 7, 3, 10, 11, 13, 14, 16, 6, 19, 20, 22, 8, 25, 9, 28, 29, 31, 32, 34, 12, 37, 38, 40, 41, 43, 15, 46, 47, 49, 17, 52, 18, 55, 56, 58, 59, 61, 21, 64, 65, 67, 23, 70, 24, 73, 74, 76, 26, 79, 27, 82, 83, 85, 86, 88, 30, 91, 92, 94

Offset: 1

Clark Kimberling

nonn

A026169 a(n) = s(k), where k is the n-th number k such that s(j)A026166.

Original entry on oeis.org

1, 2, 4, 8, 10, 16, 20, 22, 26, 28, 34, 40, 44, 46, 52, 56, 58, 62, 64, 70, 74, 76, 80, 82, 88, 94, 98, 100, 106, 112, 116, 118, 124, 128, 130, 134, 136, 142, 148, 152, 154, 160, 164, 166, 170, 172, 178, 182, 184, 188, 190, 196, 202, 206

Offset: 1

Clark Kimberling

nonn

A026204 a(n) = (1/5)*s(n), where s(n) is the n-th multiple of 5 in A026166.

Original entry on oeis.org

2, 1, 4, 8, 3, 14, 5, 16, 6, 20, 7, 26, 9, 10, 32, 11, 34, 12, 38, 13, 44, 15, 50, 17, 52, 18, 56, 19, 58, 62, 21, 22, 68, 23, 70, 24, 74, 25, 76, 80, 27, 28, 86, 29, 88, 30, 92, 31, 98, 33, 104, 35, 106, 36, 110, 37, 112, 116, 39, 40, 122

Offset: 1

Clark Kimberling

nonn

A026226 Numbers k such that A026136(k) = A026166(k).

Original entry on oeis.org

1, 7, 16, 19, 25, 34, 43, 46, 52, 55, 61, 70, 73, 79, 88, 97, 100, 106, 115, 124, 127, 133, 136, 142, 151, 154, 160, 163, 169, 178, 181, 187, 196, 205, 208, 214, 217, 223, 232, 235, 241, 250, 259, 262, 268, 277, 286, 289, 295, 298

Offset: 1

Clark Kimberling

nonn

A026229 Numbers k such that A026166(k) = A026142(k) - 2.

Original entry on oeis.org

2, 6, 12, 18, 21, 30, 36, 39, 48, 54, 57, 63, 66, 75, 84, 90, 93, 102, 108, 111, 117, 120, 129, 138, 144, 147, 156, 162, 165, 171, 174, 183, 189, 192, 198, 201, 210, 219, 225, 228, 237, 246, 252, 255, 264, 270, 273, 279, 282, 291

Offset: 1

Clark Kimberling

nonn

Cf. A026142, A026166.

Title corrected by Sean A. Irvine, Sep 22 2019

A026231 Numbers k such that A026166(k) = A026142(k) + 1.

Original entry on oeis.org

8, 17, 20, 26, 35, 44, 47, 53, 56, 62, 71, 74, 80, 89, 98, 101, 107, 116, 125, 128, 134, 137, 143, 152, 155, 161, 164, 170, 179, 182, 188, 197, 206, 209, 215, 218, 224, 233, 236, 242, 251, 260, 263, 269, 278, 287, 290, 296, 299

Offset: 1

Clark Kimberling

nonn

Cf. A026142, A026166.

Title corrected by Sean A. Irvine, Sep 22 2019

A026168 Numbers k such that A026166(j) < A026166(k) for all j < k.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 11, 12, 14, 15, 18, 21, 23, 24, 27, 29, 30, 32, 33, 36, 38, 39, 41, 42, 45, 48, 50, 51, 54, 57, 59, 60, 63, 65, 66, 68, 69, 72, 75, 77, 78, 81, 83, 84, 86, 87, 90, 92, 93, 95, 96, 99, 102, 104, 105, 108, 110, 111, 113, 114

Offset: 1

Clark Kimberling

nonn

Also a(n) is the (n-1)st number k such that A026166(k) > k, for n >= 3.

Cf. A026166.

A026228 Numbers k such that A026166(k) = A026136(k) - 1.

Original entry on oeis.org

2, 5, 11, 14, 23, 29, 32, 38, 41, 50, 59, 65, 68, 77, 83, 86, 92, 95, 104, 110, 113, 119, 122, 131, 140, 146, 149, 158, 167, 173, 176, 185, 191, 194, 200, 203, 212, 221, 227, 230, 239, 245, 248, 254, 257, 266, 272, 275, 281, 284

Offset: 1

Clark Kimberling

nonn

cp's OEIS Frontend

A026200 a(n) = (s(n) + 2)/3, where s(n) is the n-th number congruent to 1 mod 3 in A026166.

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A026167 a(n) is the position of n in A026166.

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A026202 a(n) = (1/4)*s(n), where s(n) is the n-th multiple of 4 in A026166.

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A026169 a(n) = s(k), where k is the n-th number k such that s(j)A026166.

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A026204 a(n) = (1/5)*s(n), where s(n) is the n-th multiple of 5 in A026166.

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A026226 Numbers k such that A026136(k) = A026166(k).

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A026229 Numbers k such that A026166(k) = A026142(k) - 2.

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A026231 Numbers k such that A026166(k) = A026142(k) + 1.

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A026168 Numbers k such that A026166(j) < A026166(k) for all j < k.

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A026228 Numbers k such that A026166(k) = A026136(k) - 1.

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