A138305 -id:A138305 - cp's OEIS frontend

A138306 Least prime p such that 2n = p + g, where g is a prime primitive root of p, or 0 if there is no such prime p.

0, 0, 0, 5, 7, 7, 0, 0, 11, 13, 17, 13, 0, 17, 23, 19, 23, 0, 0, 23, 23, 31, 43, 29, 37, 41, 37, 37, 41, 41, 43, 0, 47, 61, 41, 43, 67, 47, 47, 67, 59, 53, 73, 47, 47, 61, 53, 59, 67, 0, 59, 61, 59, 67, 97, 89, 97, 79, 71, 61, 79, 71, 73, 67, 71, 71, 97, 83, 71, 137, 113, 0, 103, 89

Offset: 1

T. D. Noe, Mar 14 2008

nonn

Goldbach meets prime primitive prime roots. Sequence A138118 gives the number of representations for each 2n and sequence A138307 lists the values of 2n that are not represented.

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A138305 (prime primitive roots).

A138307 Even numbers not representable as p+g, where p is a prime and g is a prime primitive root of p.

Original entry on oeis.org

2, 4, 6, 14, 16, 26, 36, 38, 64, 100, 144, 196, 206, 256, 324, 332, 400, 484, 530, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400

Offset: 1

T. D. Noe, Mar 14 2008

nonn

This sequence appears to contain the squares of all even numbers (A016742) and a thin set of other numbers (A138318).

Cf. A138305 (prime primitive roots).

A138318 Even nonsquares not representable as p+g, where p is a prime and g is a prime primitive root of p.

Original entry on oeis.org

2, 6, 14, 26, 38, 206, 332, 530, 8000, 32768, 85184, 125000, 175616

Offset: 1

T. D. Noe, Mar 14 2008

nonn

This is a subsequence of A138307. Terms starting with a(9) are cubes: 20^3, 32^3, 44^3, 50^3 and 56^3.

Cf. A138305 (prime primitive roots).

A138319 Number of ways in which 2n can be represented as p+g, where p is a prime and g is a prime primitive root of p.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 2, 3, 1, 1, 4, 1, 2, 2, 2, 3, 2, 1, 0, 1, 1, 3, 3, 1, 1, 5, 1, 3, 3, 2, 2, 2, 2, 1, 3, 1, 0, 6, 4, 1, 5, 1, 3, 3, 2, 3, 5, 2, 2, 4, 1, 6, 5, 2, 2, 4, 1, 3, 0, 2, 2, 6, 1, 3, 7, 2, 5, 6, 1, 3, 5, 3, 4, 4, 2, 2, 7, 1, 4, 1, 1, 6, 5, 1, 0, 2, 3, 4, 5, 0, 4, 7

Offset: 1

T. D. Noe, Mar 14 2008

nonn

T. D. Noe, Table of n, a(n) for n=1..10000

Cf. A138305 (prime primitive roots), A138306 (least p such that 2n=p+g).

cp's OEIS Frontend

A138306 Least prime p such that 2n = p + g, where g is a prime primitive root of p, or 0 if there is no such prime p.

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A138307 Even numbers not representable as p+g, where p is a prime and g is a prime primitive root of p.

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Author

Keywords

Comments

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A138318 Even nonsquares not representable as p+g, where p is a prime and g is a prime primitive root of p.

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Author

Keywords

Comments

Crossrefs

A138319 Number of ways in which 2n can be represented as p+g, where p is a prime and g is a prime primitive root of p.

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Author

Keywords

Links

Crossrefs