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 1-4 of 4 results.

A185167 Primes of the form k*6^m +1 where k is a Mersenne prime (A000668) and m is an integer.

Original entry on oeis.org

19, 43, 109, 1117, 3889, 40177, 139969, 326593, 839809, 4718557, 5038849, 5925313, 18874333, 52068097, 1088391169, 1874451457, 6115248577, 24461134273, 1410554953729, 2429289086977, 31701630016513, 118486616113153
Offset: 1

Views

Author

Gilbert Mozzo, Feb 18 2011

Keywords

Examples

			(2^521-1)*6^959+1 is prime

Crossrefs

Cf. A000668, A185069.

Programs

  • Magma
    // For the Mersenne prime 2^521-1, for example:
[n: n in [0..1000] | IsPrime((2^521-1)*6^n+1)];
  • Mathematica
    Union[Flatten[Table[Select[p*6^Range[0, 30] + 1, # < 10^20 && PrimeQ[#] &], {p, {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951}}]]]
Union[Flatten[Table[Select[(2^MersennePrimeExponent[n]-1)6^Range[ 0,20]+ 1,PrimeQ],{n,20}]]] (* Harvey P. Dale, Aug 15 2021 *)

Extensions

Partially edited by N. J. A. Sloane, Feb 19 2011

A186782 Primes of the form k*6^m-1 with k prime and m an integer.

Original entry on oeis.org

2, 11, 17, 29, 41, 71, 101, 107, 113, 137, 173, 179, 251, 257, 281, 317, 353, 401, 431, 467, 617, 641, 647, 653, 677, 683, 761, 821, 827, 941, 977, 1181, 1193, 1361, 1373, 1433, 1511, 1613, 1697, 1877, 1901, 1907, 2081, 2153, 2237, 2273, 2297, 2333, 2381, 2411, 2591
Offset: 1

Views

Author

Gilbert Mozzo, Feb 26 2011

Keywords

Comments

Companion sequence to A185069.

Examples

			5*6^1-1 = 29 is prime and therefore a term.
7*6^2-1 = 251 is prime and therefore a term.
17*6^13-1 = 222031798271 is prime and therefore a term (see also its companion in A185069).

Crossrefs

Cf. A185069.

Programs

  • Magma
    IsA186782:=function(n); k:=n+1; while k mod 6 eq 0 do k:=(k div 6); end while; return IsPrime(k); end function; [ n: n in PrimesUpTo(3000) | IsA186782(n) ]; // Klaus Brockhaus, Mar 01 2011
  • Mathematica
    maxM = 4; p = Prime[Range[PrimePi[2*6^maxM]]];Sort[Flatten[Table[Select[p + 1, PrimeQ[#/6^k] &], {k, 0, maxM}] - 1]] (* T. D. Noe, Feb 28 2011 *)

A186687 Primes of the form k*6^m - 1, where k is a Mersenne prime (A000668) and m >= 0.

Original entry on oeis.org

2, 17, 41, 107, 251, 647, 761, 1511, 23327, 27431, 139967, 3145721, 30233087, 35551871, 6530347007, 39182082047, 91424858111, 146766805631, 6847552083566591, 153558654482644991, 246511875008397311, 14215144014964850687
Offset: 1

Views

Author

Gilbert Mozzo, Feb 25 2011

Keywords

Comments

Twin of A185167.

Examples

			(2^1279-1)*6^1047-1 is prime.

Crossrefs

Cf. A186104, A186105, A185069, A185167.

Programs

  • Magma
    [n: n in [0..3000] | IsPrime((2^1279-1)*6^n-1)];
  • Mathematica
    Union[Flatten[Table[Select[p*6^Range[0, 30] - 1, # < 10^20 && PrimeQ[#] &], {p, {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951}}]]]

A186811 Twin primes of the form k*6^m-1 and k*6^m+1, where k is prime.

Original entry on oeis.org

11, 13, 17, 19, 29, 31, 41, 43, 71, 73, 101, 103, 107, 109, 137, 139, 179, 181, 281, 283, 431, 433, 617, 619, 641, 643, 821, 823, 827, 829, 1697, 1699, 1877, 1879, 2081, 2083, 2237, 2239, 2381, 2383, 2591, 2593
Offset: 1

Views

Author

Gilbert Mozzo, Feb 27 2011

Keywords

Comments

Twins are obtained by comparing the values given in A185069 and A186782.

Examples

			17*6^13-1 and 17*6^13+1 are twins.

Crossrefs

Cf. A185069, A186782.

Programs

  • Mathematica
    maxM = 5; r = Select[Prime[Range[PrimePi[2*6^maxM]]], PrimeQ[# + 2] &] + 1; u = Sort[Flatten[Table[Select[r,PrimeQ[#/6^k] &] - 1, {k, maxM}]]]; Sort[Join[u, u + 2]] (* T. D. Noe, Feb 28 2011 *)
Showing 1-4 of 4 results.

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

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