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.

Previous Showing 41-50 of 640 results. Next

A138841 Concatenation of initial and final digit of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 31, 17, 81, 11, 57, 27, 21, 61, 17, 17, 61, 57, 17, 17, 41, 21, 11, 27, 41, 31, 21, 41, 41, 41, 81, 57, 57, 51, 77, 17, 11, 47, 81, 61, 11, 41, 91, 17, 27, 17, 31, 11, 27, 11, 31
Offset: 1

Views

Author

Omar E. Pol, Apr 01 2008

Keywords

Examples

			a(5)=81 because the 5th Mersenne prime is 8191, A000668(5)=8191.

Crossrefs

Cf. A000668, A073729, A080172, A135613, A138840, A138842, A138843.

Formula

a(n) = A073729(A000668(n)). - Michel Marcus, Apr 17 2018

Extensions

a(40)-a(47) from Ivan Panchenko, Apr 17 2018

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 *)

A080173 Final 2 digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

3, 7, 31, 27, 91, 71, 87, 47, 51, 11, 27, 27, 51, 27, 87, 7, 51, 71, 91, 7, 11, 51, 91, 71, 51, 11, 71, 7, 7, 11, 47, 87, 91, 27, 11, 51, 71, 91, 71, 47, 7, 47, 71, 71, 27, 51, 11, 51
Offset: 1

Views

Author

Mark Dowdeswell, Feb 04 2003

Keywords

Links

Crossrefs

Cf. A080172, A000668, A000043.

Programs

  • Mathematica
    Mod[2^MersennePrimeExponent[Range[48]]-1, 100] (* Mark Dowdeswell, Sep 16 2024 *)

Extensions

Offset corrected by Arkadiusz Wesolowski, Jan 26 2012
a(39)-a(47) from Ivan Panchenko, Apr 11 2018
a(48) from Mark Dowdeswell, Sep 16 2024

A138866 Concatenation of first 3 digits and last 3 digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 3131, 127127, 819191, 131071, 524287, 214647, 230951, 618111, 162127, 170727, 686151, 531127, 104087, 147007, 446351, 259071, 190991, 285607, 478111, 346551, 281191, 431471, 448751, 402511, 854671, 536207, 521007, 512311, 746447, 174887, 129591, 412527, 814711, 623151, 127271, 437791, 924071, 125047, 299407, 122247, 315871, 124871, 202927, 169751, 316511
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

Crossrefs

Cf. A000668, A080173, A104511, A138816, A138817, A138840, A138841.

Programs

  • Mathematica
    Join[{33,77,3131},FromDigits[Flatten[Join[{Take[IntegerDigits[#],3],Take[ IntegerDigits[ #],-3]}]]]&/@ (2^MersennePrimeExponent[Range[4,40]]-1)] (* Harvey P. Dale, Dec 30 2023 *)

Extensions

More terms from Harvey P. Dale, Dec 30 2023

A139224 M(M-1)/2, where M is Mersenne prime A000668(n).

Original entry on oeis.org

3, 21, 465, 8001, 33542145, 8589737985, 137438167041, 2305843005992468481, 2658455991569831742348849606740148225, 191561942608236107294793377465333618488307184098607105
Offset: 1

Views

Author

Omar E. Pol, May 10 2008

Keywords

Comments

Perfect number A000396(n) minus Mersenne prime A000668(n).

Links

Crossrefs

Cf. A000217, A000396, A000668, A036689, A139096, A139115, A139116, A139223, A139225, A139226, A139256, A139306.

Formula

a(n) = A000668(n)*(A000668(n)-1)/2.
a(n) = A000396(n)-A000668(n).

Extensions

More terms from Max Alekseyev, Mar 09 2009

A139424 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, 1, 1, 1, 43, 1, 41, 53, 91, 317, 317, 43, 1, 37, 3595, 563, 17239, 911, 11497, 58501, 1259, 10283, 138569, 72247, 27733, 11777, 179105
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=5 prime 3=M(1)=2^2-1 so k(1)=1;
7*7-1*7-1=41 prime 7=M(2)=2^3-1 so k(2)=1;
31*31-1*31-1=929 prime 31=M(3)=2^5-1 so k(3)=1.

Crossrefs

Cf. A000668, A139425, 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 *)

Extensions

a(27)-a(28) from Robert Price, May 09 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 *)
Previous Showing 41-50 of 640 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.