A205558 -id:A205558 - cp's OEIS frontend

A205707 Prime(A205705(n)), the n-th number s(k) such that 8 divides s(k)-s(j) for some j

11, 13, 19, 19, 23, 29, 29, 31, 31, 37, 37, 37, 41, 43, 43, 43, 47, 47, 47, 53, 53, 53, 53, 59, 59, 59, 59, 61, 61, 61, 61, 61, 67, 67, 67, 67, 67, 71, 71, 71, 71, 73, 73, 79, 79, 79, 79, 79, 83, 83, 83, 83, 83, 83, 89, 89, 89, 97, 97, 97, 97, 101, 101, 101, 101

Offset: 1

Clark Kimberling, Jan 31 2012

nonn

For a guide to related sequences, see A205558.

			(See the example at A205705.)

Cf. A204890, A205705, A205558.

Mathematica
```
(See the program at A205705.)
```

A205708 Prime(A205706(n)), the n-th number s(j) such that 8 divides s(k)-s(j), where the pairs (k,j) are given by A205705 and A205706.

Original entry on oeis.org

3, 5, 3, 11, 7, 5, 13, 7, 23, 5, 13, 29, 17, 3, 11, 19, 7, 23, 31, 5, 13, 29, 37, 3, 11, 19, 43, 5, 13, 29, 37, 53, 3, 11, 19, 43, 59, 7, 23, 31, 47, 17, 41, 7, 23, 31, 47, 71, 3, 11, 19, 43, 59, 67, 17, 41, 73, 17, 41, 73, 89, 5, 13, 29, 37, 53, 61, 7, 23, 31

Offset: 1

Clark Kimberling, Jan 31 2012

nonn

For a guide to related sequences, see A205558.

			(See the example at A205705.)

Cf. A204890, A205705, A205558.

Mathematica
```
(See the program at A205705.)
```

A205711 Positions of multiples of 9 in A204890 (differences of primes).

Original entry on oeis.org

7, 31, 37, 41, 51, 63, 69, 75, 82, 92, 96, 101, 112, 123, 129, 133, 140, 150, 159, 164, 178, 187, 198, 202, 214, 224, 228, 232, 236, 241, 246, 260, 269, 273, 280, 290, 294, 298, 301, 305, 310, 315, 323, 331, 336, 344, 358, 367, 371, 375, 386, 390

Offset: 1

Clark Kimberling, Jan 31 2012

nonn

For a guide to related sequences, see A205558.

			In A204890=(1,3,2,5,4,2,9,8,6,4,11,10,8,...), multiples of 9 are in positions 7,31,37,...  See the example at A205712.

Cf. A204890, A205712, A205558.

(See the program at A205712.)
With[{prs=Prime[Range[30]]},Flatten[Position[Flatten[Table[prs[[n]]- Take[ prs,n-1],{n,2,Length[prs]}]],?(Divisible[#,9]&)]]] (* _Harvey P. Dale, Dec 01 2013 *)

A205714 Prime(A205712(n)), the n-th number s(k) such that 9 divides s(k)-s(j) for some j

Original entry on oeis.org

11, 23, 29, 29, 31, 37, 41, 41, 43, 47, 47, 47, 53, 59, 59, 59, 61, 61, 67, 67, 71, 71, 73, 73, 79, 79, 79, 83, 83, 83, 83, 89, 89, 89, 97, 97, 97, 97, 101, 101, 101, 101, 101, 103, 103, 103, 107, 107, 107, 107, 109, 109, 109, 113, 113, 113, 113, 127, 127

Offset: 1

Clark Kimberling, Jan 31 2012

nonn

For a guide to related sequences, see A205558.

			(See the example at A205712.)

Cf. A204890, A205712, A205558.

Mathematica
```
(See the program at A205712.)
```

A205715 Prime(A205713(n)), the n-th number s(j) such that 9 divides s(k)-s(j), where the pairs (k,j) are given by A205712 and A205713.

Original entry on oeis.org

2, 5, 2, 11, 13, 19, 5, 23, 7, 2, 11, 29, 17, 5, 23, 41, 7, 43, 13, 31, 17, 53, 19, 37, 7, 43, 61, 2, 11, 29, 47, 17, 53, 71, 7, 43, 61, 79, 2, 11, 29, 47, 83, 13, 31, 67, 17, 53, 71, 89, 19, 37, 73, 5, 23, 41, 59, 19, 37, 73, 109, 5, 23, 41, 59, 113, 2, 11, 29, 47

Offset: 1

Clark Kimberling, Jan 31 2012

nonn

For a guide to related sequences, see A205558.

			(See the example at A205712.)

Cf. A204890, A205712, A205558.

Mathematica
```
(See the program at A205712.)
```

A205722 Prime(A205720(n)), the n-th number s(k) such that 10 divides s(k)-s(j) for some j

Original entry on oeis.org

13, 17, 23, 23, 29, 31, 37, 37, 41, 41, 43, 43, 43, 47, 47, 47, 53, 53, 53, 53, 59, 59, 61, 61, 61, 67, 67, 67, 67, 71, 71, 71, 71, 73, 73, 73, 73, 73, 79, 79, 79, 83, 83, 83, 83, 83, 83, 89, 89, 89, 89, 97, 97, 97, 97, 97, 101, 101, 101, 101, 101, 103, 103

Offset: 1

Clark Kimberling, Jan 31 2012

nonn

For a guide to related sequences, see A205558.

			(See the example at A205720.)

Cf. A204890, A205720, A205558.

Mathematica
```
(See the program at A205720.)
```

A205723 Prime(A205721(n)), the n-th number s(j) such that 10 divides s(k)-s(j), where the pairs (k,j) are given by A205720 and A205721.

Original entry on oeis.org

3, 7, 3, 13, 19, 11, 7, 17, 11, 31, 3, 13, 23, 7, 17, 37, 3, 13, 23, 43, 19, 29, 11, 31, 41, 7, 17, 37, 47, 11, 31, 41, 61, 3, 13, 23, 43, 53, 19, 29, 59, 3, 13, 23, 43, 53, 73, 19, 29, 59, 79, 7, 17, 37, 47, 67, 11, 31, 41, 61, 71, 3, 13, 23, 43, 53, 73, 83, 7, 17

Offset: 1

Clark Kimberling, Jan 31 2012

nonn

For a guide to related sequences, see A205558.

			(See the example at A205720.)

Cf. A204890, A205720, A205558.

Mathematica
```
(See the program at A205720.)
```

A361744 A(n,k) is the least m such that there are k primes in the set {prime(n) + 2^i | 1 <= i <= m}, or -1 if no such number exists; square array A(n,k), n > 1, k >= 1, read by antidiagonals.

Original entry on oeis.org

1, 2, 1, 3, 3, 2, 4, 5, 4, 1, 6, 11, 6, 3, 2, 7, 47, 8, 5, 4, 1, 12, 53, 10, 7, 8, 13, 2, 15, 141, 16, 9, 20, 21, 6, 3, 16, 143, 18, 15, 38, 33, 30, 7, 1, 18, 191, 20, 23, 64, 81, 162, 39, 3, 4, 28, 273, 28, 29, 80, 129, 654, 79, 5, 12, 2

Offset: 2

Jean-Marc Rebert, Mar 22 2023

			p = prime(2) = 3, m=1, u = {p + 2^k | 1 <= k <= m} = {5} contains one prime, and no lesser m satisfies this, so A(2,1) = 1.
Square array A(n,k) n > 1 and k >= 1 begins:
 1,     2,     3,     4,     6,     7,    12,    15,    16,    18, ...
 1,     3,     5,    11,    47,    53,   141,   143,   191,   273, ...
 2,     4,     6,     8,    10,    16,    18,    20,    28,    30, ...
 1,     3,     5,     7,     9,    15,    23,    29,    31,    55, ...
 2,     4,     8,    20,    38,    64,    80,   292,  1132,  4108, ...
 1,    13,    21,    33,    81,   129,   285,   297,   769,  3381, ...
 2,     6,    30,   162,   654,   714,  1370,  1662,  1722,  2810, ...
 3,     7,    39,    79,   359,   451,  1031,  1039, 11311, 30227, ...
 1,     3,     5,     7,     9,    13,    15,    17,    23,    27, ...

Cf. A057732 (1st row), A094076 (1st column).
Cf. A361679.
Cf. A019434 (primes 2^n+1), A057732 (2^n+3), A059242 (2^n+5), A057195 (2^n+7), A057196(2^n+9), A102633 (2^n+11), A102634 (2^n+13), A057197 (2^n+15), A057200 (2^n+17), A057221 (2^n+19), A057201 (2^n+21), A057203 (2^n+23).
Cf. A205558 and A231232 (with 2*k instead of 2^k).

A(n, k)= {my(nb=0, p=prime(n), m=1); while (nb

cp's OEIS Frontend

A205707 Prime(A205705(n)), the n-th number s(k) such that 8 divides s(k)-s(j) for some j

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A205708 Prime(A205706(n)), the n-th number s(j) such that 8 divides s(k)-s(j), where the pairs (k,j) are given by A205705 and A205706.

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Mathematica

A205711 Positions of multiples of 9 in A204890 (differences of primes).

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Mathematica

A205714 Prime(A205712(n)), the n-th number s(k) such that 9 divides s(k)-s(j) for some j

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A205715 Prime(A205713(n)), the n-th number s(j) such that 9 divides s(k)-s(j), where the pairs (k,j) are given by A205712 and A205713.

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Mathematica

A205722 Prime(A205720(n)), the n-th number s(k) such that 10 divides s(k)-s(j) for some j

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Mathematica

A205723 Prime(A205721(n)), the n-th number s(j) such that 10 divides s(k)-s(j), where the pairs (k,j) are given by A205720 and A205721.

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Mathematica

A361744 A(n,k) is the least m such that there are k primes in the set {prime(n) + 2^i | 1 <= i <= m}, or -1 if no such number exists; square array A(n,k), n > 1, k >= 1, read by antidiagonals.

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