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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A051320 Euclid-Mullin sequence (A000945) with initial value a(1)=53 instead of a(1)=2.

Original entry on oeis.org

53, 2, 107, 3, 7, 11, 2620003, 707431, 1993, 4409, 131, 17, 5, 858127, 79, 163, 19, 46061, 31, 17707, 157, 43, 3135504913004354085487249, 9893869, 149, 1001472037, 16979051, 387853, 61, 13, 227, 41, 206779, 443, 37, 1709
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=53; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, n-1} ] ] ] ]; Array[a, 15]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=53; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 26 2015

A051321 Euclid-Mullin sequence (A000945) with initial value a(1)=59 instead of a(1)=2.

Original entry on oeis.org

59, 2, 7, 827, 3, 13, 4583, 5, 610478010871, 61, 292658543, 4483, 47, 11, 31, 43, 16453, 41, 3671, 1982639, 628319, 841476613, 449, 997793, 73, 983, 53, 28475917, 19, 673
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=59; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=59; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 04 2015

Extensions

a(28)-a(48) from Robert Price, Jul 13 2015

A051322 Euclid-Mullin sequence (A000945) with initial value a(1)=61 instead of a(1)=2.

Original entry on oeis.org

61, 2, 3, 367, 7, 5, 1217, 17, 13, 59, 3271, 19, 11, 76938833, 337, 10711, 1021, 31, 83, 1290503, 15608141, 195648590992627, 109, 15983112328343713807564263439978033717550587578630760604057976854157331
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=61; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=61; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 04 2015

A051323 Euclid-Mullin sequence (A000945) with initial value a(1)=67 instead of a(1)=2.

Original entry on oeis.org

67, 2, 3, 13, 5227, 7, 5, 4637, 107, 23, 1889, 50929, 31, 1677554191669, 538282187, 59, 37, 17046661, 81088366624779421, 11, 6242880316142699576539967984792911, 73, 17, 1187, 101, 883, 3491, 47, 83, 852851, 317, 1493, 579707, 109, 1579145715181, 179, 1618489, 331
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=67; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=67; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 06 2015

Extensions

a(21)-a(38) from Robert Price, Jul 12 2015

A051325 Euclid-Mullin sequence (A000945) with initial value a(1)=73 instead of a(1)=2.

Original entry on oeis.org

73, 2, 3, 439, 7, 5, 6729871, 103, 23, 92581, 13, 19, 2453563465139998636061911, 739, 3167, 47356379285063777, 463, 3673, 2918137, 41, 17, 2307841395358410336056217199460000033494100011180619106269258300884070797073446703818111
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=73; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=73; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 06 2015

A051326 Euclid-Mullin sequence (A000945) with initial value a(1)=79 instead of a(1)=2.

Original entry on oeis.org

79, 2, 3, 5, 2371, 7, 39334891, 19, 29397438602292811, 43, 167, 839, 5839, 30402153456526009093473029504929376787635911, 241815479790331, 41, 180922657, 5303, 2389, 13, 31, 11
Offset: 1

Views

Author

Labos Elemer

Keywords

Comments

a(23) is a 122-digit prime.
a(5), a(7), a(9), a(14) and a(23) are all the product of the preceding terms + 1. - Robert Price, Jul 10 2015
a(32) requires factoring a composite 292 digit integer. - Robert Price, Sep 05 2021

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266, A020639.

Programs

  • Mathematica
    a[1]=79; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f
first(m)=my(v=vector(m)); v[1]=79; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 06 2015

Formula

a(n) = A020639(1 + Product_{k=1..n-1} a(k)), a(1) = 79.

A051327 Euclid-Mullin sequence (A000945) with initial value a(1)=83 instead of a(1)=2.

Original entry on oeis.org

83, 2, 167, 3, 7, 67, 5, 13, 719, 37, 11, 31, 1367, 31440216015620321911, 988487183108868589955299792587646370011, 19, 499, 937, 23, 29, 863, 1852812869, 1157393039341097158113740816072403984079, 445807, 13833892959043, 359, 109, 331
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=83; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    gpf(n)=my(f=factor(n)[, 1]); f[#f];
first(m)=my(v=vector(m)); v[1]=83; for(i=2, m, v[i]=gpf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 25 2015

Extensions

More terms from Sean A. Irvine, Apr 12 2011

A051331 Euclid-Mullin sequence (A000945) with initial value a(1)=131071 instead of a(1)=2.

Original entry on oeis.org

131071, 2, 3, 43, 31, 113, 5, 13, 4391, 7, 8012161, 3090097, 17, 809, 83843, 18743, 29, 179, 2347, 83, 97883, 14411, 12109, 97, 25951, 5506100565736709510249607377685096261432096111292821492562747465234861171
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=131071; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    gpf(n)=my(f=factor(n)[, 1]); f[#f];
first(m)=my(v=vector(m)); v[1]=131071; for(i=2, m, v[i]=gpf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Nov 25 2015

A051332 Euclid-Mullin sequence (A000945) with initial value a(1)=65537 instead of a(1)=2.

Original entry on oeis.org

65537, 2, 5, 3, 7, 11, 61, 13, 120052642711, 157, 8837, 71, 3271, 31, 37, 19, 8597, 8868542017, 23, 149, 26443389827415776296437975011182059459845296976025400711, 97, 751, 17, 280121, 4999, 8797543, 12241, 29, 53, 197, 5659, 3109, 1063, 727915549
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A020639, A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=65537; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f \\ A020639
first(m)=my(v=vector(m)); v[1]=65537; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 07 2015

Extensions

a(25)-a(35) from Robert Price, Jul 09 2015

A051333 Euclid-Mullin sequence (A000945) with initial value a(1)=257 instead of a(1)=2.

Original entry on oeis.org

257, 2, 5, 3, 11, 84811, 31, 7, 1560842137471, 20113, 17, 83, 47, 339491, 7814561, 109, 2897, 16103, 70921439, 199, 1381, 34987489236924545883729121, 43, 241, 37, 491, 28468486915378661, 8803, 29, 25212511, 2311, 67, 3929, 1151, 192697, 797, 157, 23, 1489, 13
Offset: 1

Views

Author

Labos Elemer

Keywords

Links

Crossrefs

Cf. A020639, A000945, A000946, A005265, A005266.

Programs

  • Mathematica
    a[1]=257; a[n_] := First[ Flatten[ FactorInteger[ 1+Product[ a[ j ], {j, 1, n-1} ] ] ] ]; Array[a, 10]
  • PARI
    spf(n)=my(f=factor(n)[1, 1]); f \\ A020639
first(m)=my(v=vector(m)); v[1]=257; for(i=2, m, v[i]=spf(1+prod(j=1, i-1, v[j]))); v \\ Anders Hellström, Dec 07 2015

Extensions

a(22)-a(27) from Robert Price, Jul 09 2015
a(28)-a(40) from Tyler Busby, Oct 12 2023
Previous Showing 31-40 of 46 results. Next

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

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