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.

A124516 a(n) = least k such that 2^i*k-1 is prime for 1<=i<=n.

Original entry on oeis.org

2, 2, 3, 3, 45, 45, 561330, 9549960, 42932385, 13044904290, 277344139215, 277344139215, 2045466215756535
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Crossrefs

Cf. A006254, A124485, A124493, A124494, A124017, A125113, A124514, A124515.
Cf. A071576, A101994, A101320.

Programs

  • Mathematica
    k = 1; Do[If[n < 5, inc = 1, inc = 15];If[Mod[k, inc] > 0, k = k + inc - Mod[k, inc]];While[Nand @@ PrimeQ[Table[2^j, {j, n}]*k - 1], k += inc]; Print[k], {n, 1, 10}] (* Ray Chandler *)

Extensions

Definition corrected and a(10) calculated by Farideh Firoozbakht, Nov 24 2006
a(11)-a(13) from Giovanni Resta, Apr 22 2019

A124514 Numbers k for which 2*k-1, 4*k-1, 8*k-1, 16*k-1, 32*k-1, 64*k-1 and 128*k-1 are primes.

Original entry on oeis.org

561330, 1082115, 1164735, 5128905, 5154945, 6157350, 7015155, 7072770, 9549960, 11551830, 12088065, 14421825, 18544365, 19099920, 21194760, 24580050, 25392720, 26277285, 31400085, 34359030, 42932385, 44087025, 47915595
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Links

Crossrefs

Cf. A006254, A124485, A124493, A124494, A124017, A125113, A124515, A124516.

Programs

  • Mathematica
    Select[15*Range[3200000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32, 64, 128}*# - 1) &] (* Ray Chandler, Nov 22 2006 *)
apQ[n_]:=AllTrue[NestList[2#&,2n,6]-1,PrimeQ]; Select[15*Range[ 32*10^5], apQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 08 2019 *)

A124017 Numbers n for which 2n-1, 4n-1, 8n-1, 16n-1 and 32n-1 are primes.

Original entry on oeis.org

45, 90, 26820, 26925, 30705, 31710, 33375, 63420, 63570, 71805, 83865, 93075, 103185, 127140, 134025, 148050, 170460, 202635, 211035, 223305, 269505, 297225, 303660, 329175, 335625, 362505, 387975, 405270, 405405, 406425, 409755, 463335
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Links

Crossrefs

Cf. A006254, A124485, A124493, A124494, A125113, A124514, A124515, A124516.

Programs

  • Mathematica
    Select[15*Range[40000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32}*# - 1) &] (* Ray Chandler, Nov 22 2006 *)
Select[15*Range[31000],AllTrue[#*2^Range[5]-1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 05 2019 *)

A124493 Numbers k for which 2*k-1, 4*k-1 and 8*k-1 are primes.

Original entry on oeis.org

3, 6, 21, 45, 90, 180, 255, 360, 510, 516, 615, 705, 726, 741, 756, 906, 945, 951, 966, 1230, 1350, 1410, 1725, 1746, 1770, 1911, 1956, 2541, 2700, 2721, 2925, 3051, 3066, 3225, 3540, 3576, 3675, 3951, 4485, 4611, 5295, 5346, 5355, 5586, 5736, 5775, 5901
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Links

Crossrefs

Cf. A006254, A124485, A124494, A124017, A125113, A124514, A124515, A124516.

Programs

  • Mathematica
    Select[3*Range[2000], And @@ PrimeQ /@ ({2, 4, 8}*# - 1) &] (* Ray Chandler, Nov 22 2006 *)

A124494 Numbers k for which 2*k-1, 4*k-1, 8*k-1 and 16*k-1 are primes.

Original entry on oeis.org

3, 45, 90, 180, 255, 615, 705, 1350, 1770, 3225, 5295, 5775, 5955, 6060, 8580, 9855, 9945, 11175, 13095, 13740, 15195, 21825, 26820, 26925, 27615, 28920, 30075, 30705, 31710, 33375, 35700, 37350, 37665, 41250, 43770, 49185, 50700, 52185, 53640
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Links

Crossrefs

Cf. A006254, A124485, A125113, A124514, A124515, A124516.
Subsequence of A124493. Supersequence of A124017.

Programs

  • Mathematica
    Select[3*Range[20000], And @@ PrimeQ /@ ({2, 4, 8, 16}*# - 1) &] (* Ray Chandler, Nov 22 2006 *)
Select[Range[3,55000,3],AllTrue[2^Range[4] #-1,PrimeQ]&] (* or, faster  *) Join[{3},Select[Range[ 15,55000,15],AllTrue[ 2^Range[4] #-1,PrimeQ]&]] (* Harvey P. Dale, Feb 02 2025 *)

Extensions

Extended by Ray Chandler, Nov 22 2006

A124515 Numbers k for which 2*k-1, 4*k-1, 8*k-1, 16*k-1, 32*k-1, 64*k-1, 128*k-1 and 256*k-1 are primes.

Original entry on oeis.org

9549960, 26277285, 42932385, 85864770, 99239790, 113183070, 152596290, 172159515, 198479580, 237059175, 287482065, 305192580, 342533490, 382203030, 542591115, 563002110, 597825570, 686106720, 742227135, 786875025, 1135145760
Offset: 1

Views

Author

Artur Jasinski, Nov 04 2006

Keywords

Links

Crossrefs

Cf. A006254, A124485, A124493, A124494, A124017, A125113, A124514, A124516.

Programs

  • Mathematica
    Select[15*Range[76000000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32, 64, 128, 256}*# - 1) &] (* Ray Chandler, Nov 22 2006 *)

Extensions

Extended by Ray Chandler, Nov 22 2006

A339580 Indices of records in A339579.

Original entry on oeis.org

1, 3, 90, 1122660, 19099920, 85864770, 26089808580, 554688278430, 4090932431513070, 95405042230542330
Offset: 1

Views

Author

N. J. A. Sloane, Dec 24 2020

Keywords

Comments

The records themselves begin 4,5,6,7,8,9,10,12,13,14.
a(11) <= 90616211958465842220.

Examples

			90 is in the sequence as A339579(90) = 6 (90*2^k - 1 is prime for k = 0..5 and composite for k = 6) and A339579(m) < 6 for m < 90. - _David A. Corneth_, Dec 24 2020

References

  • Carl Pomerance, Problem 81:21 (= 321), in R. K. Guy problem list.

Links

Crossrefs

Cf. A063377, A124514, A125113, A339579, A339581.

Formula

a(n) = A339581(n) + 1 for n >= 2. - David A. Corneth, Dec 24 2020

Extensions

a(8)-a(10) were taken from A057331 and the bound on a(11) was taken from A005602. - David A. Corneth and Amiram Eldar, Dec 25 2020
Showing 1-7 of 7 results.

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

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