A047392 -id:A047392 - cp's OEIS frontend

A187232 Rank transform of the sequence floor(7n/4); complement of A187233.

1, 3, 5, 7, 9, 11, 13, 15, 16, 19, 20, 23, 24, 26, 28, 30, 32, 34, 36, 38, 39, 41, 44, 46, 47, 49, 51, 53, 55, 57, 59, 61, 62, 64, 66, 69, 70, 72, 74, 76, 78, 80, 82, 84, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 177, 179, 181, 183

Offset: 1

Clark Kimberling, Mar 07 2011

nonn

See A187224. A187232(n)=A187907(n) for n=1,2,...,20; A187232(21)=39 and A187907(21)=40.

Cf. A187224, A187233.

seqA=Table[Floor[7n/4],{n,1,220}] (*A047392*)
seqB=Table[n,{n,1,220}];(*A000027*)
jointRank[{seqA_,seqB_}]:={Flatten@Position[#1,{,1}],Flatten@Position[#1,{,2}]}&[Sort@Flatten[{{#1,1}&/@seqA,{#1,2}&/@seqB},1]];
limseqU=FixedPoint[jointRank[{seqA,#1[[1]]}]&,jointRank[{seqA,seqB}]][[1]] (*A187232*)
Complement[Range[Length[seqA]],limseqU] (*A187233*)
(*by Peter J. C. Moses, Mar 07 2011*)

A272915 a(n) = n + floor(5*n/6).

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 53, 55, 56, 58, 60, 62, 64, 66, 67, 69, 71, 73, 75, 77, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 100, 102, 104, 106, 108, 110, 111, 113, 115, 117, 119

Offset: 0

Bruno Berselli, Jun 15 2016

Equivalently, numbers congruent to {0, 1, 3, 5, 7, 9} mod 11.

In general, n + floor((k-1)*n/k) provides the numbers congruent to {0, 1, 3, 5, ..., 2*k-3} mod (2*k-1) for k>1.

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Cf. similar sequences with formula n+floor((k-1)*n/k): A032766 (k=2), A047220 (k=3), A047392 (k=4), A187318 (k=5).

Magma
```
[n+Floor(5*n/6): n in [0..70]];
```
Mathematica
```
Table[n + Floor[5 n/6], {n, 0, 70}]
```
Maxima
```
makelist(n+floor(5*n/6), n, 0, 70);
```
PARI
```
vector(70, n, n--; n+floor(5*n/6))
```
Python
```
[n+int(5*n/6) for n in range(70)]
```
Sage
```
[n+floor(5*n/6) for n in range(70)];
```

G.f.: x*(1 + 2 x + 2 x^2 + 2 x^3 + 2 x^4 + 2 x^5)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5)).
a(n) = a(n-1) + a(n-6) - a(n-7).
a(6*k + r) = 11*k + 2*r - (1 - (-1)^a(r))/2, with r = 0..5.

cp's OEIS Frontend

A187232 Rank transform of the sequence floor(7n/4); complement of A187233.

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A272915 a(n) = n + floor(5*n/6).

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Mathematica

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