A124516 -id:A124516 - cp's OEIS frontend

A071576 a(n) = least k such that 2ik + 1 is prime for all 1 <= i <= n.

1, 1, 1, 165, 5415, 12705, 256410, 256410, 6480303060, 217245863835, 946622690475, 35511547806735, 439116128090640, 5714676453270219435

Offset: 1

Benoit Cloitre, May 31 2002

Cf. A088250, A124516, A124522, A124522, A063983.

Cf. A005097, A123998, A124408-A124411.

k = 1; Do[ While[p = Table[2*i*k + 1, {i, 1, n}]; Union[ PrimeQ[p]] != {True}, k++ ]; Print[k], {n, 1, 15}] (* Robert G. Wilson v *)

for(n=1,6,s=1; while(sum(i=1,n,isprime(2*s*i+1))

Extended by Robert G. Wilson v, Jun 06 2002
a(9) from Ryan Propper, Jun 20 2005
a(10)-a(13) from Don Reble, Nov 05 2006
a(14) from Giovanni Resta, Apr 01 2017

A124514 Numbers k for which 2k-1, 4k-1, 8k-1, 16k-1, 32k-1, 64k-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

Artur Jasinski, Nov 04 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1000

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

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 *)

A125113 Numbers n such that 2n-1, 4n-1, 8n-1, 16n-1, 32n-1 and 64n-1 are primes.

Original entry on oeis.org

45, 31710, 63570, 202635, 405405, 534600, 561330, 589305, 666945, 799350, 903045, 979125, 1082115, 1122660, 1164735, 1303035, 1424475, 1620645, 1669995, 1892100, 1981020, 2044440, 2164230, 2222415, 2329470, 2332125, 2447445, 2448855

Offset: 1

Artur Jasinski, Nov 22 2006

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A006254, A124485, A124493, A124494, A124017, A124514, A124515, A124516.

Select[15*Range[200000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32, 64}*# - 1) &] (* Ray Chandler, Nov 22 2006 *)
Select[15*Range[164000],AllTrue[# 2^Range[6]-1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 20 2020 *)

Extended by Ray Chandler, Nov 22 2006

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

Artur Jasinski, Nov 04 2006

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

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 2k-1, 4k-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

Artur Jasinski, Nov 04 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

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

A124494 Numbers k for which 2k-1, 4k-1, 8k-1 and 16k-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

Artur Jasinski, Nov 04 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Subsequence of A124493. Supersequence of A124017.

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 *)

Extended by Ray Chandler, Nov 22 2006

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

Artur Jasinski, Nov 04 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..1000

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

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

Extended by Ray Chandler, Nov 22 2006

A244435 a(n) is the smallest number m such that 2km - 1 is composite for all k, 0 < k < n+1.

Original entry on oeis.org

5, 13, 13, 62, 73, 73, 89, 118, 118, 118, 118, 118, 236, 926, 959, 959, 959, 959, 959, 959, 1063, 1474, 1474, 1474, 1667, 1667, 6118, 8249, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 9098, 35573, 35573, 35573, 57448, 57448, 57448, 57448, 57448, 57448, 57448

Offset: 1

Farideh Firoozbakht, Jul 19 2014

nonn

a(2)=a(3)=13, a(5)=a(6)=73, ... a(29)=a(30)=...=a(43)=9098, ... . A244436 gives numbers k such that a(k) is not in the set {a(k-1), a(k+1)}.

Robert Israel, Table of n, a(n) for n = 1..164

Cf. A124516, A244433, A244436.

M:= 0: R:= NULL:
for m from 2 while M < 100 do
  for i from 0 while not isprime(2*i*m-1) do od:
  if i-1 > M then R:= R, m$(i-1-M); M:= i-1; fi;
od:
R; # Robert Israel, May 03 2021

isok(n, m) = for(k=1, n, my(x=2*k*m-1); if ((x==1) || isprime(x), return(0))); return (1);
a(n) = my(m=1); while(!isok(n, m), m++); m; \\ Michel Marcus, May 04 2021

A305740 a(n) is the smallest k such that 10^m*k + 1 is prime for all m in 1..n.

Original entry on oeis.org

1, 1, 4, 7, 7, 170716, 170926, 26373004, 247201983, 10562770680, 118345066231, 54717848613610

Offset: 1

Jon E. Schoenfield, Jun 23 2018

a(12) > 3*10^11.

			10^1*1 + 1 = 11 (prime), so a(1) = 1.
10^2*1 + 1 = 101 (also prime), so a(2) = 1 as well.
10^3*1 + 1 = 1001 = 7*143, so a(3) > 1;
10^1*2 + 1 = 21 = 3*7, so a(3) > 2;
10^2*3 + 1 = 301 = 7*43, so a(3) > 3;
however, for m = 1..3, 10^m*4 + 1 yields 41, 401, and 4001, each of which is prime, so a(3) = 4.

Cf. A000040 (primes), A124417, A124516.

a(12) from Giovanni Resta, Jun 25 2018

cp's OEIS Frontend

A071576 a(n) = least k such that 2ik + 1 is prime for all 1 <= i <= n.

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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.

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A125113 Numbers n such that 2n-1, 4n-1, 8n-1, 16n-1, 32n-1 and 64n-1 are primes.

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

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

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Mathematica

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

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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.

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A244435 a(n) is the smallest number m such that 2*k*m - 1 is composite for all k, 0 < k < n+1.

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Maple

PARI

A305740 a(n) is the smallest k such that 10^m*k + 1 is prime for all m in 1..n.

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Examples

Crossrefs

Extensions

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

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

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

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

A244435 a(n) is the smallest number m such that 2km - 1 is composite for all k, 0 < k < n+1.