A124417 -id:A124417 - cp's OEIS frontend

A124041 Numbers k such that 2k+1, 4k+1 and 8*k+1 are primes.

9, 39, 165, 219, 249, 309, 414, 534, 639, 765, 1044, 1065, 1089, 1155, 1395, 1509, 1530, 1554, 1590, 1884, 2079, 2115, 2130, 2310, 2319, 2430, 2475, 2709, 2874, 3060, 3105, 3354, 3420, 3684, 3705, 3780, 3819, 4104, 4314, 4554, 4599, 4659, 4869, 5160

Offset: 1

Artur Jasinski, Nov 02 2006

nonn

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

Cf. A005097, A123998, A124412-A124417.

Select[3*Range[2000], And @@ PrimeQ /@ ({2, 4, 8}*# + 1) &] (* Ray Chandler, Dec 06 2006 *)

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

A089761 Smallest k such that k*i^2 + 1 is prime for i = 1 to n.

Original entry on oeis.org

1, 1, 4, 22, 58, 58, 58, 54972, 68112, 4748632, 861066640, 861066640, 861066640, 861066640, 861066640

Offset: 1

Amarnath Murthy, Nov 22 2003

a(16) > 1.4*10^13. [Max Alekseyev]

Cf. A124417.

for n from 1 to 10 do for k from 1 do f:=0: for i from 1 to n do if not isprime(k*i^2+1) then f:=1: break fi od: if f=0 then printf("%d, ",k): break fi od od: # C. Ronaldo

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 26 2004

a(11)-a(15) from Donovan Johnson, Sep 27 2008

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

A124041 Numbers k such that 2*k+1, 4*k+1 and 8*k+1 are primes.

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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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A089761 Smallest k such that k*i^2 + 1 is prime for i = 1 to n.

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Maple

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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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Extensions

A124041 Numbers k such that 2k+1, 4k+1 and 8*k+1 are primes.

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.