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.

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

A080172 Final digit of n-th Mersenne prime A000668(n).

Original entry on oeis.org

3, 7, 1, 7, 1, 1, 7, 7, 1, 1, 7, 7, 1, 7, 7, 7, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 7, 7, 1, 7, 7, 1, 7, 1, 1, 1, 1, 1, 7, 7, 7, 1, 1, 7, 1, 1, 1
Offset: 1

Views

Author

Mark Dowdeswell, Feb 04 2003

Keywords

Comments

Distribution of final digit for Mersenne primes appears (naturally) to be different from distribution for regular primes. Unconfirmed 49th, 50th and 51st digits in sequence are 1, 1, 1 (awaiting confirmation of 49th, 50th and 51st Mersenne primes).

References

  • G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 16.

Links

Crossrefs

Cf. A000668, A007652, A080173.

Programs

  • Maple
    (Maple code from N. J. A. Sloane) # let s1 := list of terms in A000043
f:=n->if n mod 4 = 0 then 4 else n mod 4; fi; map(x->2^f(x)-1,s1);
  • Mathematica
    Mod[2^MersennePrimeExponent[Range[48]]-1,10] (* Harvey P. Dale, Aug 09 2023; updated by Mark Dowdeswell, Sep 16 2024 *)

Extensions

Updated by N. J. A. Sloane, Apr 01 2008
a(40)-a(47) from Ivan Panchenko, Apr 11 2018
a(48) from Mark Dowdeswell, Sep 16 2024

A138864 First 3 digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

3, 7, 31, 127, 819, 131, 524, 214, 230, 618, 162, 170, 686, 531, 104, 147, 446, 259, 190, 285, 478, 346, 281, 431, 448, 402, 854, 536, 521, 512, 746, 174, 129, 412, 814, 623, 127, 437, 924, 125, 299, 122, 315, 124, 202, 169, 316
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

Crossrefs

Cf. A000668, A080173, A104511, A138863, A138864, A138865, A138866.

Extensions

a(40)-a(47) from Ivan Panchenko, Aug 03 2018

A138863 Concatenation of first two digits and last two digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 3131, 1227, 8191, 1371, 5287, 2147, 2351, 6111, 1627, 1727, 6851, 5327, 1087, 1407, 4451, 2571, 1991, 2807, 4711, 3451, 2891, 4371, 4451, 4011, 8571, 5307, 5207, 5111, 7447, 1787, 1291, 4127, 8111, 6251, 1271, 4391, 9271, 1247, 2907, 1247, 3171, 1271, 2027, 1651, 3111
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

Crossrefs

Cf. A000668, A080173, A104511, A138816, A138817, A138840, A138841, A138862, A138864, A138865, A138866.

Extensions

More terms from Jinyuan Wang, Mar 14 2020

A138862 First two (i.e., the two most significant) digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

3, 7, 31, 12, 81, 13, 52, 21, 23, 61, 16, 17, 68, 53, 10, 14, 44, 25, 19, 28, 47, 34, 28, 43, 44, 40, 85, 53, 52, 51, 74, 17, 12, 41, 81, 62, 12, 43, 92, 12, 29, 12, 31, 12, 20, 16, 31
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

Crossrefs

Cf. A000668, A080173, A138863, A138864, A138865, A138866.

Programs

  • Mathematica
    Join[{3,7},FromDigits[Take[IntegerDigits[#],2]]&/@ (2^MersennePrimeExponent[ Range[ 3,47]]-1)] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 01 2020 *)

Extensions

a(40)-a(47) from Ivan Panchenko, Aug 03 2018
Definition clarified by Harvey P. Dale, Aug 01 2020

A138865 Last 3 digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

3, 7, 31, 127, 191, 71, 287, 647, 951, 111, 127, 727, 151, 127, 87, 7, 351, 71, 991, 607, 111, 551, 191, 471, 751, 511, 671, 207, 7, 311, 447, 887, 591, 527, 711, 151, 271, 791, 71, 47, 407, 247, 871, 871, 927, 751, 511
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

Crossrefs

Cf. A000668, A080173, A104511, A138862, A138863, A138864, A138866.

Programs

  • Mathematica
    Array[Mod[2^MersennePrimeExponent[#] - 1, 1000] &, 45] (* Michael De Vlieger, Aug 05 2018 *)

Extensions

a(40)-a(47) from Ivan Panchenko, Apr 03 2018

A138874 Last two digits of the n-th even perfect number.

Original entry on oeis.org

6, 28, 96, 28, 36, 56, 28, 28, 76, 16, 28, 28, 76, 28, 28, 28, 76, 56, 36, 28, 16, 76, 36, 56, 76, 16, 56, 28, 28, 16, 28, 28, 36, 28, 16, 76, 56, 36, 56, 28, 28, 28, 56, 56, 28, 76, 16
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

  • Édouard Lucas: Théorie des nombres. Vol. 1: Le calcul des nombres entiers. Le calcul des nombres rationnels. La divisibilité arithmétique. Paris: Gauthier-Villars, 1891, Nr. 229 (Théorème de Fermat), Ex. V, p. 424-425.
  • Omar E. Pol, Los numeros perfectos

Crossrefs

Cf. A000396, A080173, A104511, A138875.

Extensions

Definition changed (inserting the word "even") and a(39)-a(47) added by Ivan Panchenko, Aug 04 2018
Showing 1-7 of 7 results.

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