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.

A093869 Frequency of occurrence of prime(n) in A093868.

Original entry on oeis.org

2, 2, 1, 1, 3, 2, 3, 1, 3, 3, 1, 3, 3, 1, 3, 5, 3, 2, 5, 3, 2, 3, 3, 3, 3, 5, 1, 3, 2, 4, 4, 3, 3, 1, 3, 2, 3, 3, 3, 5, 3, 2, 3, 2, 3, 1, 3, 3, 3, 2, 4, 4, 2, 3, 3, 3, 5, 1, 4, 5, 3, 5, 5, 3, 2, 3, 3, 3, 3, 2, 6, 3, 6, 6, 3, 3, 3, 3, 3, 4, 3, 2, 5, 2, 4, 3, 3, 3, 3, 1, 3, 4, 4, 5, 3, 3, 7, 4, 1, 3, 5, 3, 4, 3, 3
Offset: 1

Views

Author

Amarnath Murthy, Apr 20 2004

Keywords

Crossrefs

Cf. A093868.

Extensions

Corrected by Rick L. Shepherd, Aug 23 2004
More terms from David Wasserman, Apr 23 2007

A194603 Smallest prime either of the form n*2^k - 1 or n*2^k + 1, k >= 0, or 0 if no such prime exists.

Original entry on oeis.org

2, 3, 2, 3, 11, 5, 13, 7, 17, 11, 23, 11, 53, 13, 29, 17, 67, 17, 37, 19, 41, 23, 47, 23, 101, 53, 53, 29, 59, 29, 61, 31, 67, 67, 71, 37, 73, 37, 79, 41, 83, 41, 173, 43, 89, 47, 751, 47, 97, 101, 101, 53, 107, 53, 109, 113, 113, 59, 1889, 59, 487, 61, 127
Offset: 1

Views

Author

Arkadiusz Wesolowski, Aug 30 2011

Keywords

Comments

Primes arising from A194591 (or 0 if no such prime exists).
Many of these terms are in A093868.

Examples

			For n=7, 7*2^0-1 and 7*2^0+1 are composite, but 7*2^1-1=13 is prime, so a(7)=13.

Links

Crossrefs

Cf. A194591, A194600, A194606, A194607, A194608, A194635, A194636, A194637, A194638, A194639.
Cf. A038699, A050921, A076335, A180247.

Programs

  • Mathematica
    Table[k = 0; While[! PrimeQ[a = n*2^k - 1] && ! PrimeQ[a = n*2^k + 1], k++]; a, {n, 100}] (* Arkadiusz Wesolowski, Sep 04 2011 *)
n2k[n_]:=Module[{k=0},While[NoneTrue[n*2^k+{1,-1},PrimeQ],k++];SelectFirst[ n*2^k+{-1,1},PrimeQ]]; Array[n2k,70] (* The program uses the NoneTrue and SelectFirst functions from Mathematica version 10 *) (* Harvey P. Dale, Jun 03 2015 *)

A140180 A number n is included if the smallest prime that is congruent to 1 (mod n) is <= the smallest prime that is congruent to -1 (mod n).

Original entry on oeis.org

1, 2, 5, 10, 11, 13, 16, 22, 23, 25, 26, 28, 29, 33, 35, 36, 39, 40, 41, 43, 46, 50, 52, 53, 56, 58, 61, 63, 65, 66, 67, 70, 73, 78, 81, 82, 83, 86, 88, 89, 92, 93, 95, 96, 100, 101, 105, 106, 111, 112, 113, 116, 119, 122, 124, 125, 126, 127, 130, 131, 134, 136, 145
Offset: 1

Views

Author

Leroy Quet, May 11 2008

Keywords

Examples

			For n = 1 and 2 the smallest prime that is congruent to 1 (mod n) equals the smallest prime that is congruent to -1 (mod n). For all other n the inequality is strict.

Links

Crossrefs

Cf. A093868, A140181.

Extensions

More terms from Diana L. Mecum, Jul 04 2008

A140181 A number n is included if the smallest prime that is congruent to 1 (mod n) is >= the smallest prime that is congruent to -1 (mod n).

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 15, 17, 18, 19, 20, 21, 24, 27, 30, 31, 32, 34, 37, 38, 42, 44, 45, 47, 48, 49, 51, 54, 55, 57, 59, 60, 62, 64, 68, 69, 71, 72, 74, 75, 76, 77, 79, 80, 84, 85, 87, 90, 91, 94, 97, 98, 99, 102, 103, 104, 107, 108, 109, 110, 114, 115, 117
Offset: 1

Views

Author

Leroy Quet, May 11 2008

Keywords

Examples

			For n = 1 and 2 the smallest prime that is congruent to 1 (mod n) equals the smallest prime that is congruent to -1 (mod n). For all other n the inequality is strict.

Links

Crossrefs

Cf. A093868, A140180.

Extensions

More terms from Diana L. Mecum, Jul 04 2008
Showing 1-4 of 4 results.

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

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