A212037 -id:A212037 - cp's OEIS frontend

A214501 The size of the set of numbers k>=0 such that all (3^n-k)2^n-1 are prime but only the last (largest) (3^n-k)2^n+1 is also an associated twin prime.

1, 2, 1, 1, 2, 1, 1, 6, 1, 2, 1, 6, 8, 8, 41, 11, 5, 8, 11, 24, 35, 15, 22, 5, 11, 19, 15, 16, 60, 10, 21, 35, 82, 13, 8, 4, 1, 44, 4, 33, 12, 29, 59, 45, 17, 60, 4, 1, 119, 38, 6, 35, 1, 29, 48, 100, 72, 31, 128, 27, 33, 29, 41, 14, 21, 40, 19, 52, 36, 79, 54

Offset: 1

Pierre CAMI, Jul 20 2012

nonn

Starting at a count of zero, we consider for increasing k>=0 the pairs (3^n-k)*2^n+-1. If the smaller of these two numbers is prime, we increase the counter. If the larger of these two numbers is also prime, we admit the counter to the sequence. It is basically a measure of how many unsuccessful primality tests on the larger of the two numbers are done before it becomes a compatible twin prime.

Heuristically, the average of a(n)/n over n=1 to N tends to 0.61 as N increases.

Pierre CAMI, Table of n, a(n) for n = 1..500

Cf. A212037, A214497, A214498, A214502.

A214502 The size of the set of numbers k>=0 such that all (3^n+k)2^n-1 are prime but only the last (largest) (3^n+k)2^n+1 is also an associated twin prime.

Original entry on oeis.org

1, 3, 2, 5, 16, 2, 2, 18, 2, 8, 8, 10, 14, 9, 5, 43, 15, 1, 56, 13, 5, 151, 7, 20, 107, 3, 30, 8, 16, 31, 8, 21, 3, 103, 57, 38, 28, 37, 99, 5, 15, 50, 87, 31, 67, 107, 1, 113, 69, 12, 41, 19, 23, 43, 150, 100, 49, 76, 3, 159, 48, 86, 49, 81, 62, 48, 118, 66

Offset: 1

Pierre CAMI, Jul 20 2012

nonn

Starting at a count of zero, we consider for increasing k>=0 the pairs (3^n+k)*2^n+-1. If the smaller of these two numbers is prime, we increase the counter. If the larger of these two numbers is also prime, we admit the counter to the sequence. It is basically a measure of how many unsuccessful primality tests on the larger of the two numbers are done before it becomes a compatible twin prime.

Pierre CAMI, Table of n, a(n) for n = 1..500

Cf. A212037, A214497, A214498, A214501.

A214499 The size of the set of numbers k>=0 such that all (3^n-k)3^n-1 are prime but only the last (largest) (3^n-k)3^n+1 is also an associated twin prime.

Original entry on oeis.org

1, 1, 4, 4, 1, 1, 2, 3, 4, 6, 4, 6, 4, 11, 3, 10, 6, 9, 4, 18, 30, 16, 8, 29, 5, 32, 21, 15, 45, 5, 97, 10, 36, 3, 33, 35, 55, 20, 54, 25, 30, 30, 36, 8, 38, 30, 16, 6, 3, 20, 10, 35, 36, 2, 84, 20, 52, 85, 25, 25, 70, 46, 15, 53, 6, 103, 11, 27, 87, 15, 42, 14

Offset: 1

Pierre CAMI, Jul 20 2012

nonn

Starting at a count of zero, we consider for increasing k>=0 the pairs (3^n-k)*3^n+-1. If the smaller of these two numbers is prime, we increase the counter. If the larger of these two numbers is also prime, we admit the counter to the sequence. It is basically a measure of how many unsuccessful primality tests on the larger of the two numbers are done before it becomes a compatible twin prime.

Heuristically, the average of a(n)/n over n=1 to N tends to 0.83 as N increases.

Pierre CAMI, Table of n, a(n) for n = 1..500

Cf. A212037, A214495, A214496, A214500, A214501, A214502.

A212038 The size of the set of numbers k>=0 such that all (2^n-k)2^n-1 are prime but only (2^n-k)2^n+1 with the largest k is also the associated twin prime.

Original entry on oeis.org

1, 7, 5, 2, 4, 11, 6, 1, 3, 2, 31, 2, 11, 11, 11, 6, 30, 16, 2, 36, 90, 56, 11, 52, 13, 36, 10, 62, 20, 31, 23, 28, 30, 14, 47, 22, 10, 5, 104, 39, 11, 14, 64, 184, 209, 176, 193, 162, 25, 38, 23, 5, 27, 157, 5, 17, 32, 90, 1, 199, 96, 83, 29, 82, 12, 220, 19, 40, 37, 13, 16, 120, 11, 130, 12, 77, 202

Offset: 4

Pierre CAMI, Jul 14 2012

nonn

Search set similar to A212037 but the sign of k in the prime form is switched.

Heuristically the average of a(n)/n for n=1 to N tends to 1 as N increases.

Pierre CAMI, Table of n, a(n) for n = 4..825

Cf. A191619, A191620, A205322.

A212038 := proc(n)
    local a,k,p ;
    a := 0 ;
    for k from 0 do
        p := (2^n-k)*2^n-1 ;
        if isprime(p) then
            a := a+1 ;
        end if;
        if isprime(p) and isprime(p+2) then
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 21 2012

SCRIPT
DIM nn, 3
DIM jj
DIM kk
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
IF nn>825 THEN END
SET kk, -1
SET jj, 0
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP (2^nn-kk)*2^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
SET jj, jj+1
PRP (2^nn-kk)*2^nn+1, tt
IF ISPRP THEN GOTO d
IF ISPRIME THEN GOTO d
GOTO loopk
LABEL d
SETS tt, %d, %d\,; nn; jj
WRITE myfile, tt
GOTO loopn

A214500 The size of the set of numbers k>=0 such that all (3^n+k)3^n-1 are prime but only the last (largest) (3^n+k)3^n+1 is also an associated twin prime.

Original entry on oeis.org

1, 2, 1, 2, 3, 3, 9, 3, 4, 1, 8, 20, 4, 10, 24, 8, 17, 9, 28, 16, 19, 6, 33, 19, 12, 5, 49, 27, 25, 26, 10, 91, 143, 9, 41, 14, 36, 11, 34, 26, 28, 10, 50, 7, 12, 11, 8, 27, 13, 4, 44, 138, 50, 10, 45, 21, 51, 84, 65, 48, 39, 139, 36, 19, 22, 85, 113, 105, 5, 36

Offset: 1

Pierre CAMI, Jul 20 2012

nonn

Starting at a count of zero, we consider for increasing k>=0 the pairs (3^n+k)*3^n+-1. If the smaller of these two numbers is prime, we increase the counter. If the larger of these two numbers is also prime, we admit the counter to the sequence. It is basically a measure of how many unsuccessful primality tests on the larger of the two numbers are done before it becomes a compatible twin prime.

Heuristically, the average of a(n)/n over n=1 to N tends to 0.83 as N increases.

Cf. A212037, A214495, A214496, A214499.

cp's OEIS Frontend

A214501 The size of the set of numbers k>=0 such that all (3^n-k)2^n-1 are prime but only the last (largest) (3^n-k)2^n+1 is also an associated twin prime.

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A214502 The size of the set of numbers k>=0 such that all (3^n+k)2^n-1 are prime but only the last (largest) (3^n+k)2^n+1 is also an associated twin prime.

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A214499 The size of the set of numbers k>=0 such that all (3^n-k)3^n-1 are prime but only the last (largest) (3^n-k)3^n+1 is also an associated twin prime.

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A212038 The size of the set of numbers k>=0 such that all (2^n-k)2^n-1 are prime but only (2^n-k)2^n+1 with the largest k is also the associated twin prime.

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PFGW

A214500 The size of the set of numbers k>=0 such that all (3^n+k)3^n-1 are prime but only the last (largest) (3^n+k)3^n+1 is also an associated twin prime.

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Author

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cp's OEIS Frontend

A214501 The size of the set of numbers k>=0 such that all (3^n-k)*2^n-1 are prime but only the last (largest) (3^n-k)*2^n+1 is also an associated twin prime.

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A214502 The size of the set of numbers k>=0 such that all (3^n+k)*2^n-1 are prime but only the last (largest) (3^n+k)*2^n+1 is also an associated twin prime.

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Author

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A214499 The size of the set of numbers k>=0 such that all (3^n-k)*3^n-1 are prime but only the last (largest) (3^n-k)*3^n+1 is also an associated twin prime.

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Author

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A212038 The size of the set of numbers k>=0 such that all (2^n-k)*2^n-1 are prime but only (2^n-k)*2^n+1 with the largest k is also the associated twin prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

PFGW

A214500 The size of the set of numbers k>=0 such that all (3^n+k)*3^n-1 are prime but only the last (largest) (3^n+k)*3^n+1 is also an associated twin prime.

Views

Author

Keywords

Comments

Crossrefs

A214501 The size of the set of numbers k>=0 such that all (3^n-k)2^n-1 are prime but only the last (largest) (3^n-k)2^n+1 is also an associated twin prime.

A214502 The size of the set of numbers k>=0 such that all (3^n+k)2^n-1 are prime but only the last (largest) (3^n+k)2^n+1 is also an associated twin prime.

A214499 The size of the set of numbers k>=0 such that all (3^n-k)3^n-1 are prime but only the last (largest) (3^n-k)3^n+1 is also an associated twin prime.

A212038 The size of the set of numbers k>=0 such that all (2^n-k)2^n-1 are prime but only (2^n-k)2^n+1 with the largest k is also the associated twin prime.

A214500 The size of the set of numbers k>=0 such that all (3^n+k)3^n-1 are prime but only the last (largest) (3^n+k)3^n+1 is also an associated twin prime.