A204892 -id:A204892 - cp's OEIS frontend

A204984 a(n) = (1/n)*A204983(n).

1, 1, 1, 1, 3, 1, 1, 1, 7, 3, 93, 1, 315, 1, 1, 1, 15, 7, 13797, 3, 3, 93, 89, 1, 41943, 315, 9709, 1, 9256395, 1, 1, 1, 31, 15, 117, 7, 1857283155, 13797, 105, 3, 25575, 3, 381, 93, 91, 89, 178481, 1, 42799, 41943, 5, 315, 84973577874915, 9709, 19065, 1, 4599, 9256395

Offset: 1

Clark Kimberling, Jan 21 2012

nonn

For a guide to related sequences, see A204892.

Cf. A204979, A204892, A204983.

Cf. A023758 (when a(n)=1).

Mathematica
```
(See the program at A204979.)
```

a(n) = for (k=1, oo, for (j=1, k-1, my(d=2^(k-1)-2^(j-1)); if (!(d % n), return(d/n)););); \\ Michel Marcus, Sep 16 2023

More terms from Michel Marcus, Sep 16 2023

A204985 Ordered differences of numbers 2^k for k>=1.

Original entry on oeis.org

2, 6, 4, 14, 12, 8, 30, 28, 24, 16, 62, 60, 56, 48, 32, 126, 124, 120, 112, 96, 64, 254, 252, 248, 240, 224, 192, 128, 510, 508, 504, 496, 480, 448, 384, 256, 1022, 1020, 1016, 1008, 992, 960, 896, 768, 512, 2046, 2044, 2040, 2032, 2016, 1984, 1920

Offset: 1

Clark Kimberling, Jan 21 2012

nonn

A204985=2*A130328. For a guide to related sequences, see A204892.

Cf. A204987, A204892.

Mathematica
```
(See the program at A204987.)
```

A205014 s(k)-s(j), where (s(k),s(j)) is the least pair of central binomial coefficients for which n divides their difference.

Original entry on oeis.org

1, 4, 18, 4, 5, 18, 14, 64, 18, 50, 2508, 672, 182, 14, 3180, 64, 68, 18, 19, 3180, 672, 2508, 69, 672, 50, 182, 918, 672, 232, 3180, 520676, 64, 2508, 68, 3430, 48600, 48618, 2508, 9438, 12800, 246, 672, 115000920, 2508, 48600, 184736, 3431

Offset: 1

Clark Kimberling, Jan 22 2012

nonn

For a guide to related sequences, see A204892.

Cf. A205010, A204892.

Mathematica
```
(See the program at A205010.)
```

A205031 s(k)-s(j), where (s(k),s(j)) is the least pair of oblong numbers for which n divides their difference.

Original entry on oeis.org

4, 4, 6, 4, 10, 6, 14, 8, 18, 10, 22, 24, 26, 14, 30, 16, 34, 18, 38, 40, 42, 22, 46, 24, 50, 26, 54, 28, 58, 30, 62, 32, 66, 34, 70, 36, 74, 38, 78, 40, 82, 42, 86, 44, 90, 46, 94, 48, 98, 50, 102, 52, 106, 54, 110, 112, 114, 58, 118, 60

Offset: 1

Clark Kimberling, Jan 22 2012

nonn

For a guide to related sequences, see A204892.

Cf. A205018, A204892.

Mathematica
```
(See the program at A205018.)
```

A205032 a(n) = (s(k)-s(j))/n, where (s(k),s(j)) is the least pair of oblong numbers (A002378) for which n divides their difference; a(n) = (1/n)*A205031(n).

Original entry on oeis.org

4, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2

Offset: 1

Clark Kimberling, Jan 22 2012

nonn

For a guide to related sequences, see A204892.

Even n such that a(n) = 2 are: 2, 12, 20, 56, 72, 132, 156, 240, 272, 380, 552, 812, 992, 1056, 1332, 1640, 1892, 2256, 2756, 3540, 3660, 4032, 4160, 4556, 5112, 5256, 6320, 6972, 7656, 7832, ... - Antti Karttunen, Nov 06 2018

Antti Karttunen, Table of n, a(n) for n = 1..14025

Cf. A002378, A205018, A205031, A204892.

Cf. also A204897, A204999, A205007.

Mathematica
```
(See the program at A205018.)
```

A205032(n) = for(k=2,oo,my(sk=k*(k+1)); for(j=1,k-1,if(!((sk-((j+1)*j))%n),return((sk-((j+1)*j))/n)))); \\ Antti Karttunen, Nov 06 2018

A205032(n) = for(k=sqrtint(n)-1,oo,my(sk=k*(k+1), d); for(j=1,k-1,d=(sk-((j+1)*j)); if(0==(d%n),return(d/n),if(dAntti Karttunen, Nov 06 2018

Definition edited and more terms from Antti Karttunen, Nov 06 2018

A205103 k!!-j!!, where (k!!,j!!) is the least pair of double factorials for which n divides their difference.

Original entry on oeis.org

1, 2, 6, 12, 5, 6, 7, 40, 45, 40, 33, 12, 13, 14, 45, 336, 102, 90, 57, 40, 336, 42240, 46, 336, 3825, 104, 3456, 336, 645105, 90, 279, 3456, 33, 102, 840, 3456, 46065, 3838, 897, 40, 369, 336, 2026977, 42240, 45, 46, 47, 336, 10290, 9450, 102, 104

Offset: 1

Clark Kimberling, Jan 22 2012

nonn

For a guide to related sequences, see A204892.

Cf. A204982, A204892.

Mathematica
```
(See the program at A204982.)
```

A205110 s(k)-s(j), where (s(k),s(j)) is the least pair of numbers given by s(j)=3^j-2^j which n divides their difference.

Original entry on oeis.org

4, 4, 18, 4, 60, 18, 14, 64, 18, 60, 660, 60, 2054, 14, 60, 64, 646, 18, 646, 60, 210, 660, 46, 192, 600, 2054, 19170, 1848, 1586126, 60, 17112, 64, 660, 646, 210, 6300, 19166, 646, 6240, 600, 1394, 210, 508174, 660, 6300, 46, 5640, 192, 2058, 600

Offset: 1

Clark Kimberling, Jan 22 2012

nonn

For a guide to related sequences, see A204892.

Cf. A205000, A204892.

Mathematica
```
(See the program at A205000.)
```

A205117 The number s(j) such that n divides s(k)-s(j), where s(j) is the j-th Lucas number and k is the least positive integer for which such a j with 0

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 4, 3, 11, 1, 7, 11, 3, 4, 3, 11, 1, 11, 47, 7, 18, 7, 1, 4, 4, 3, 47, 1, 18, 3, 843, 7, 1, 29, 18, 11, 3, 47, 4, 7, 76, 3, 4, 3, 7, 1, 29, 7, 3, 7, 11, 1, 4, 47, 47, 11, 322, 18, 76, 3

Offset: 1

Clark Kimberling, Jan 22 2012

For a guide to related sequences, see A204892.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A205114, A204892.

lucas:= gfun:-rectoproc({a(n)=a(n-1)+a(n-2),a(0)=2, a(1)=1},a(n),remember):
f:= proc(n) local j,k,S,t;
    S:= [];
    for k from 1 do
      t:= lucas(k) mod n;
      if member(t,S,j) then return lucas(j) fi;
      S:= [op(S),t];
    od
end proc:
map(f, [$1..100]); # Robert Israel, Jan 21 2018

Mathematica
```
(See the program at A205114.)
```

Name corrected by Robert Israel, Jan 21 2018

A205118 s(k)-s(j), where (s(k),s(j)) is the least pair of Lucas numbers for which n divides their difference.

Original entry on oeis.org

2, 2, 3, 4, 10, 6, 7, 8, 18, 10, 11, 36, 26, 14, 15, 112, 17, 18, 76, 40, 105, 22, 46, 72, 25, 26, 2160, 28, 29, 120, 1364, 192, 198, 170, 105, 36, 518, 76, 195, 40, 123, 840, 43, 44, 315, 46, 47, 192, 196, 2200, 510, 520, 318, 2160, 275, 112, 3249, 58

Offset: 1

Clark Kimberling, Jan 22 2012

nonn

For a guide to related sequences, see A204892.

Cf. A205114, A204892.

Mathematica
```
(See the program at A205114.)
```

A205126 s(k)-s(j), where (s(k),s(j)) is the least such pair for which n divides their difference, and s(j)= j*(2^(j-1)).

Original entry on oeis.org

3, 8, 3, 8, 20, 48, 28, 8, 180, 20, 11, 48, 416, 28, 180, 48, 68, 180, 76, 20, 5040, 1012, 368, 48, 2300, 416, 11232, 28, 1856, 180, 31, 160, 1023, 68, 5040, 180, 444, 76, 11232, 160, 41984, 5040, 524256, 1012, 180, 368, 188, 48, 2303, 2300, 1020

Offset: 1

Clark Kimberling, Jan 25 2012

nonn

For a guide to related sequences, see A204892.

Cf. A205122, A204892.

Mathematica
```
(See the program at A205122.)
```

cp's OEIS Frontend

A204984 a(n) = (1/n)*A204983(n).

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A204985 Ordered differences of numbers 2^k for k>=1.

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Mathematica

A205014 s(k)-s(j), where (s(k),s(j)) is the least pair of central binomial coefficients for which n divides their difference.

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Mathematica

A205031 s(k)-s(j), where (s(k),s(j)) is the least pair of oblong numbers for which n divides their difference.

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Mathematica

A205032 a(n) = (s(k)-s(j))/n, where (s(k),s(j)) is the least pair of oblong numbers (A002378) for which n divides their difference; a(n) = (1/n)*A205031(n).

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Mathematica

PARI

PARI

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A205103 k!!-j!!, where (k!!,j!!) is the least pair of double factorials for which n divides their difference.

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Mathematica

A205110 s(k)-s(j), where (s(k),s(j)) is the least pair of numbers given by s(j)=3^j-2^j which n divides their difference.

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Mathematica

A205117 The number s(j) such that n divides s(k)-s(j), where s(j) is the j-th Lucas number and k is the least positive integer for which such a j with 0

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Maple

Mathematica

Extensions

A205118 s(k)-s(j), where (s(k),s(j)) is the least pair of Lucas numbers for which n divides their difference.

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