cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A139426 Smallest number k such that M(n)^2+k*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

Original entry on oeis.org

1, 5, 1, 5, 11, 11, 17, 19, 23, 97, 127, 145, 167, 269, 767, 479, 3307, 1453, 18007, 2357, 599, 17669, 5527, 3191, 3251, 70249, 147773, 39637
Offset: 1

Views

Author

Pierre CAMI, Apr 21 2008

Keywords

Comments

All primes certified using openpfgw_v12 from primeform group.

Examples

			3*3+1*3-1=11 prime 3=M(1)=2^2-1 so k(1)=1;
7*7+5*7-1=83 prime 7=M(2)=2^3-1 so k(2)=5;
31*31+1*31-1=991 prime 31=M(3)=2^5-1 so k(3)=1.

Crossrefs

Cf. A000668, A139424, A139425, A139427, A139428, A139429, A139430, A139421, A143385.

Programs

  • Mathematica
    A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; k = 1;
While[! PrimeQ[m2 + k*m - 1], k++]; k, {n, 15}] (* Robert Price, Apr 17 2019 *)

Extensions

3 more terms. - Pierre CAMI, Aug 11 2008

A139430 Smallest prime p such that M(n)^2+p*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

Original entry on oeis.org

3, 5, 11, 5, 11, 11, 17, 19, 23, 97, 127, 1009, 167, 269, 953, 479, 3307, 1453, 37507, 2357, 599, 17669, 5527, 3191, 3251, 70249, 147773
Offset: 1

Views

Author

Pierre CAMI, Apr 21 2008

Keywords

Comments

All primes certified using openpfgw_v12 from primeform group

Examples

			3*3+3*3-1=17 prime 3=M(1)=2^2-1 so p(1)=3;
7*7+5*7-1=83 prime 7=M(2)=2^3-1 so p(2)=5:
31*31+11*31-1=1301 prime 31=M(3)=2^5-1 so p(3)=11.

Crossrefs

Cf. A000668, A139424, A139425, A139426, A139427, A139428, A139429, A139431.

Programs

  • Mathematica
    A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; p = 1;
While[! PrimeQ[m2 + Prime[p]*m - 1], p++]; Prime[p], {n, 18}] (* Robert Price, Apr 17 2019 *)

A139425 Smallest number k such that M(n)^2-k*M(n)+1 is prime with M(n)= Mersenne primes =A000668(n).

Original entry on oeis.org

1, 1, 9, 3, 3, 25, 7, 21, 435, 241, 3, 153, 151, 493, 537, 2871, 1713, 4941, 4963, 307, 28413, 5035, 1615, 43525, 9973
Offset: 1

Views

Author

Pierre CAMI, Apr 21 2008

Keywords

Comments

All primes certified using openpfgw_v12 from primeform group

Examples

			3*3-1*3+1=7 prime 3=M(1)=2^2-1 so k(1)=1;
7*7-1*7+1=43 prime 7=M(2)=2^3-1 so k(2)=1;
31*31-9*31+1=683 prime 31=M(3)=2^5-1 so k(3)=9.

Crossrefs

Cf. A000668, A139424, A139426, A139427, A139428, A139429, A139430, A139421.

Programs

  • Mathematica
    A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; k = 1;
While[! PrimeQ[m2 - k*m + 1], k++]; k, {n, 15}] (* Robert Price, Apr 17 2019 *)

A139427 Smallest number k such that M(n)^2+k*M(n)+1 is prime with M(n)= Mersenne primes =A000668(n).

Original entry on oeis.org

1, 3, 5, 17, 17, 5, 83, 63, 71, 101, 543, 59, 569, 1029, 353, 1851, 2801, 2619, 525, 2907, 8955, 437, 30159, 5409, 8355
Offset: 1

Views

Author

Pierre CAMI, Apr 21 2008

Keywords

Comments

All primes certified using openpfgw_v12 from primeform group

Examples

			3*3+1*3+1=13 prime 3=M(1)=2^2-1 so k(1)=1;
7*7+3*7+1=71 prime 7=M(2)=2^3-1 so k(2)=3;
31*31+5*31+1=1117 prime 31=M(3)=2^5-1 so k(3)=5.

Crossrefs

Cf. A000668, A139424, A139425, A139426, A139428, A139429, A139430, A139421.

Programs

  • Mathematica
    A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; k = 1;
While[! PrimeQ[m2 + k*m + 1], k++]; k, {n, 15}] (* Robert Price, Apr 17 2019 *)

A139428 Smallest prime p such that M(n)^2-p*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

Original entry on oeis.org

5, 7, 5, 17, 43, 67, 41, 53, 311, 317, 317, 43, 1427, 37, 25693, 563, 17239, 911, 11497, 112247, 1259, 190639, 138569, 296713, 27733, 11777
Offset: 2

Views

Author

Pierre CAMI, Apr 21 2008

Keywords

Comments

All primes certified using openpfgw_v12 from primeform group

Examples

			7*7-5*7-1=13 prime 7=M(2)=2^3-1 so k(2)=5;
31*31-7*31-1=743 prime 31=M(3)=2^5-1 so k(3)=7.

Crossrefs

Cf. A000668, A139424, A139425, A139426, A139427, A139429, A139430, A139421.

Programs

  • Mathematica
    A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; p = 1;
While[! PrimeQ[m2 - Prime[p]*m - 1], p++];
Prime[p], {n, 15}] (* Robert Price, Apr 17 2019 *)

A139429 Smallest prime p such that M(n)^2 - p*M(n) + 1 is prime with M(n) = A000668(n).

Original entry on oeis.org

3, 19, 3, 3, 73, 7, 271, 1021, 241, 3, 487, 151, 2971, 35839, 5737, 1723, 81943, 115741, 307, 151549, 231823, 443431, 195163, 9973, 114913, 362599
Offset: 2

Views

Author

Pierre CAMI, Apr 21 2008

Keywords

Comments

All primes certified using openpfgw_v12 from primeform group.

Examples

			7*7-3*7+1=29 prime 7=M(2)=2^3-1 so k(2)=3;
31*31-19*31+1=373 prime 31=M(3)=2^5-1 so k(3)=19.

Crossrefs

Cf. A000668, A139424, A139425, A139426, A139427, A139428, A139430, A139421.

Programs

  • Mathematica
    A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; p = 1;
While[! PrimeQ[m2 - Prime[p]*m + 1], p++];
Prime[p], {n, 15}] (* Robert Price, Apr 17 2019 *)

A139431 Smallest prime p such that M(n)^2+p*M(n)+1 is prime with M(n)= Mersenne primes =A000668(n).

Original entry on oeis.org

3, 3, 5, 17, 17, 5, 83, 503, 71, 101, 947, 59, 569, 1787, 353, 17093, 2801, 3359, 25097, 9323, 491837, 97367, 209567, 21221, 273857, 462947, 216719
Offset: 1

Views

Author

Pierre CAMI, Apr 21 2008

Keywords

Comments

All primes certified using openpfgw_v12 from primeform group

Examples

			3*3+3*3+1=19 prime 3=M(1)=2^2-1 so p(1)=3;
7*7+3*7+1=71 prime 7=M(2)=2^3-1 so p(2)=3;
31*31+5*31+1=1117 prime 31=M(3)=2^5-1 so p(3)=5.

Crossrefs

Cf. A000668, A139424, A139425, A139426, A139427, A139428, A139429, A139430.

Programs

  • Mathematica
    A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};
Table[m = 2^A000043[[n]] - 1; m2 = m^2; p = 1;
While[! PrimeQ[m2 + Prime[p]*m + 1], p++];
Prime[p], {n, 15}] (* Robert Price, Apr 17 2019 *)
Showing 1-7 of 7 results.

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