A191620 -id:A191620 - cp's OEIS frontend

A201132 Least k such that (5^n - k)*5^n - 1 is a prime number.

1, 1, 11, 1, 17, 11, 5, 25, 43, 25, 49, 29, 25, 19, 1, 1, 55, 41, 95, 19, 11, 49, 91, 1, 83, 115, 17, 17, 119, 151, 253, 77, 293, 77, 35, 41, 29, 295, 5, 23, 433, 149, 61, 173, 113, 101, 77, 109, 19, 161, 5, 85, 53, 443, 61, 151, 1, 253, 77, 37, 55, 251, 163

Offset: 1

Michel Lagneau, Nov 27 2011

nonn

Cf. A191620, A200922.

Table[k = 0; While[!PrimeQ[(5^n - k)*5^n - 1], k++]; k, {n, 85}]

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

A201459 Least k such that (7^n - k)*7^n - 1 is a prime number.

Original entry on oeis.org

1, 1, 5, 7, 7, 11, 5, 29, 13, 29, 5, 1, 77, 1, 13, 101, 65, 77, 175, 29, 77, 121, 49, 23, 41, 31, 613, 101, 13, 37, 127, 47, 197, 31, 107, 97, 275, 17, 619, 47, 7, 199, 85, 31, 47, 17, 97, 253, 17, 37, 5, 103, 215, 119, 335, 257, 277, 121, 313, 89, 157, 187, 25, 7, 571, 11, 197, 53, 13, 101, 49, 199, 67, 389, 109, 13, 25, 41, 337, 647, 77

Offset: 1

Michel Lagneau, Dec 01 2011

nonn

Cf. A191620, A200922, A201132.

 Table[k = 0; While[!PrimeQ[(7^n - k)*7^n - 1], k++]; k, {n, 85}]

cp's OEIS Frontend

A201132 Least k such that (5^n - k)*5^n - 1 is a prime number.

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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

A201459 Least k such that (7^n - k)*7^n - 1 is a prime number.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

cp's OEIS Frontend

A201132 Least k such that (5^n - k)*5^n - 1 is a prime number.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

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

A201459 Least k such that (7^n - k)*7^n - 1 is a prime number.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

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.