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.

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A139298 a(n) = 2^(2p - 1)/4, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

8, 2048, 576460752303423488, 3618502788666131106986593281521497120414687020801267626233049500247285301248
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000668, A139294, A139295, A139296, A139297, A139299, A139300, A139301, A139302, A139303, A139304, A139305, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 5); Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = 2^(2*A000668(n) - 1)/4 = A139294(n)/4.

A139299 a(n) = 2^(2p - 1)/4-1, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

7, 2047, 576460752303423487, 3618502788666131106986593281521497120414687020801267626233049500247285301247
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139300, A139301, A139302, A139303, A139304, A139305, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 5) - 1; Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = 2^(2*A000668(n)-1)/4-1 = A139294(n)/4-1 = A139298(n)-1.

Extensions

a(4) from Amiram Eldar, Jul 10 2025

A139300 a(n) = 2^(2p - 1)/8, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

4, 1024, 288230376151711744, 1809251394333065553493296640760748560207343510400633813116524750123642650624
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139301, A139302, A139303, A139304, A139305, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 6); Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = 2^(2*A000668(n)-1)/8 = A139294(n)/8.

Extensions

a(4) from Amiram Eldar, Jul 10 2025

A139301 a(n) = (2^(2p - 1)/8)-1, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

3, 1023, 288230376151711743, 1809251394333065553493296640760748560207343510400633813116524750123642650623
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139302, A139303, A139304, A139305, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 6) - 1; Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = (2^(2*A000668(n)-1)/8)-1 = (A139294(n)/8)-1.

Extensions

a(4) from Amiram Eldar, Jul 10 2025

A139302 a(n) = 2^(2p - 1)/16, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

2, 512, 144115188075855872, 904625697166532776746648320380374280103671755200316906558262375061821325312
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139303, A139304, A139305, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 7); Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = 2^(2*A000668(n)-1)/16 = A139294(n)/16.

Extensions

a(4) from Amiram Eldar, Jul 10 2025

A139303 a(n) = (2^(2p - 1)/16)-1, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

1, 511, 144115188075855871, 904625697166532776746648320380374280103671755200316906558262375061821325311
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139302, A139304, A139305, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 7) - 1; Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = (2^(2*A000668(n)-1)/16)-1 = (A139294(n)/16)-1.

Extensions

a(4) from Amiram Eldar, Jul 10 2025

A139304 a(n) = 2^(2p - 1)/32, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

1, 256, 72057594037927936, 452312848583266388373324160190187140051835877600158453279131187530910662656
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Crossrefs

Cf. A000668, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139302, A139303, A139305, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 8); Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = 2^(2*A000668(n)-1)/32 = A139294(n)/32.

Extensions

a(4) from Amiram Eldar, Jul 10 2025

A139305 a(n) = (2^(2p - 1)/32)-1, where p is the n-th Mersenne prime A000668(n).

Original entry on oeis.org

0, 255, 72057594037927935, 452312848583266388373324160190187140051835877600158453279131187530910662655
Offset: 1

Views

Author

Omar E. Pol, Apr 13 2008

Keywords

Comments

Next term is too large to list here.

Crossrefs

Cf. A000668, A139286, A139294, A139295, A139296, A139297, A139298, A139299, A139300, A139301, A139302, A139303, A139304, A139306.

Programs

  • Mathematica
    a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 8) - 1; Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)

Formula

a(n) = (2^(2*A000668(n)-1)/32)-1 = (A139294(n)/32)-1.

Extensions

Edited by Max Alekseyev, Apr 23 2010

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

A330819 Numbers of the form M_p^2(M^p+2)^2, where M_p is a Mersenne prime (A000668) and p is a Mersenne exponent (A000043). Also the first element of the spectral basis of A330817.

Original entry on oeis.org

225, 3969, 1046529, 268402689, 4503599493152769, 295147905144993087489, 75557863725364567605249, 21267647932558653957237540927630737409, 28269553036454149273332760011886696242605918383730576346715242738439159809
Offset: 1

Views

Author

Walter Kehowski, Jan 01 2020

Keywords

Comments

The second element of the spectral basis of A330817 is A330820.

Examples

			If p=2, then M_2=3, and a(1) = 3^2(3+2)^2 = 15^2 = 225.

Links

Crossrefs

Cf. A000043, A000668, A132794, A133049, A330817, A330818, A330820.

Programs

  • Maple
    A330819:=[]:
for www to 1 do
for i from 1 to 31 do
  #ithprime(31)=127
  p:=ithprime(i);
  q:=2^p-1;
  if isprime(q) then x:=2^(2*p+1)*q^2; A330819:=[op(A330819),x]; fi;
od;
od;
A330819;
  • Mathematica
    (m = 2^MersennePrimeExponent[Range[9]] - 1)^2 * (m + 2)^2 (* Amiram Eldar, Jan 03 2020 *)

Formula

a(n) = A000668(n)^2*(A000668(n)+2)^2.
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