A124041 -id:A124041 - cp's OEIS frontend

A124417 a(n) = least k such that 2^i*k+1 is prime for 1<=i<=n.

1, 1, 9, 765, 765, 8325, 8325, 7757430, 428547690, 102764221560, 694561346985, 108428872433310, 379041973928475, 34628781572140470, 34628781572140470

Offset: 1

Artur Jasinski, Nov 02 2006

Cf. A005097, A123998, A124041, A124412, A124413, A124414, A124415, A124416.

k = 1; Do[If[n < 3, inc = 1,If[n == 3, inc = 3, 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, 15}] (* Ray Chandler, Nov 21 2006 *)

Edited by Ray Chandler, Nov 21 2006
a(10) from Farideh Firoozbakht, Nov 25 2006
a(11)-a(15) from Giovanni Resta, Apr 24 2019

A124412 Numbers k such that 2k+1, 4k+1, 8k+1 and 16k+1 are primes.

Original entry on oeis.org

765, 1065, 1155, 1530, 3105, 3420, 3705, 5160, 6840, 7695, 8325, 9060, 11265, 11505, 12195, 14835, 15390, 15885, 16650, 17655, 20745, 22185, 23205, 27300, 28155, 28995, 30165, 30690, 33300, 33825, 39015, 41715, 42690, 44370, 48465, 49935

Offset: 1

Artur Jasinski, Nov 02 2006

nonn

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

Cf. A005097, A123998, A124041, A124413-A124417.

Select[15*Range[3500], And @@ PrimeQ /@ ({2, 4, 8, 16}*# + 1) &] (* Ray Chandler, Nov 21 2006 *)

A124413 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1 and 32*k+1 are primes.

Original entry on oeis.org

765, 3420, 7695, 8325, 16650, 22185, 28995, 33300, 41715, 52935, 72510, 75075, 82950, 99810, 104715, 106425, 115620, 121275, 145635, 159840, 165900, 173070, 188745, 190815, 192795, 222870, 225705, 239400, 240510, 253395, 253890, 256410

Offset: 1

Artur Jasinski, Nov 02 2006

nonn

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

Cf. A005097, A123998, A124041, A124412-A124417.

Select[15*Range[20000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32}*# + 1) &] (* Ray Chandler, Nov 21 2006 *)

A124414 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1, 32k+1 and 64k+1 are primes.

Original entry on oeis.org

8325, 16650, 82950, 165900, 192795, 222870, 239400, 290235, 601560, 884220, 971685, 1020600, 1065570, 1120470, 1170330, 1196715, 1263360, 1638735, 1768440, 1811940, 1940190, 1948815, 2061810, 2207685, 2240940, 2639295, 2830905

Offset: 1

Artur Jasinski, Nov 02 2006

nonn

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

Cf. A005097, A123998, A124041, A124412-A124417.

Select[15*Range[200000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32, 64}*# + 1) &] (* Ray Chandler, Nov 21 2006 *)

A124415 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1, 32k+1, 64k+1 and 128*k+1 are primes.

Original entry on oeis.org

8325, 82950, 884220, 1120470, 3441690, 5627895, 5765505, 7664745, 7757430, 8555040, 10739505, 11891625, 15514860, 15623475, 18268455, 22631970, 24833775, 27373410, 29342895, 31286970, 31577205, 50077455, 51541035, 58646520

Offset: 1

Artur Jasinski, Nov 02 2006

nonn

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

Cf. A005097, A123998, A124041, A124412-A124417.

Select[15*Range[4000000], And @@ PrimeQ /@ ({2, 4, 8, 16, 32, 64, 128}*# + 1) &] (* Ray Chandler, Nov 21 2006 *)
Select[Range[15,59*10^6,15],AllTrue[2^Range[7] #+1,PrimeQ]&]  (* Harvey P. Dale, Jan 19 2025 *)

Corrected and extended by Ray Chandler, Nov 21 2006

A124416 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1, 32k+1, 64k+1, 128k+1 and 256k+1 are primes.

Original entry on oeis.org

7757430, 31286970, 360821505, 365536215, 414779430, 418803000, 428547690, 428823900, 434768475, 508654155, 584808795, 732681630, 809814510, 846079035, 857095380, 968314215, 1115279880, 1187901285, 1193371860, 1244805450

Offset: 1

Artur Jasinski, Nov 02 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..100

Cf. A005097, A123998, A124041, A124412-A124417.

Select[15*Range[10^8], And @@ PrimeQ /@ ({2, 4, 8, 16, 32, 64, 128, 256}*# + 1) &] (* Ray Chandler, Nov 21 2006 *)
Select[15*Range[83*10^6],AllTrue[#*2^Range[8]+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 23 2020 *)

Extended by Ray Chandler, Nov 21 2006

cp's OEIS Frontend

A124417 a(n) = least k such that 2^i*k+1 is prime for 1<=i<=n.

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A124412 Numbers k such that 2*k+1, 4*k+1, 8*k+1 and 16*k+1 are primes.

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A124413 Numbers k such that 2*k+1, 4*k+1, 8*k+1, 16*k+1 and 32*k+1 are primes.

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A124414 Numbers k such that 2*k+1, 4*k+1, 8*k+1, 16*k+1, 32*k+1 and 64*k+1 are primes.

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A124415 Numbers k such that 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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A124416 Numbers k such that 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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Author

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Mathematica

Extensions

A124412 Numbers k such that 2k+1, 4k+1, 8k+1 and 16k+1 are primes.

A124413 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1 and 32*k+1 are primes.

A124414 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1, 32k+1 and 64k+1 are primes.

A124415 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1, 32k+1, 64k+1 and 128*k+1 are primes.

A124416 Numbers k such that 2k+1, 4k+1, 8k+1, 16k+1, 32k+1, 64k+1, 128k+1 and 256k+1 are primes.