A124409 -id:A124409 - cp's OEIS frontend

A123998 Numbers k such that 2k+1 and 4k+1 are primes.

1, 3, 9, 15, 18, 39, 48, 69, 78, 99, 105, 114, 135, 153, 165, 168, 183, 189, 219, 249, 273, 288, 300, 303, 309, 330, 345, 363, 405, 414, 438, 468, 483, 498, 504, 534, 585, 618, 639, 648, 699, 714, 729, 765, 804, 813, 828, 879, 933, 1005, 1014, 1044, 1065, 1068

Offset: 1

Artur Jasinski, Oct 31 2006

Note that if n == 1 (mod 3) then 2n+1 is not prime (except n=1); and if n == 2 (mod 3) then 4n+1 is not prime. Therefore n must be a multiple of 3, except for n=1. - Max Alekseyev, Nov 02 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
J. O'Rourke, Why are this operator's primes the Sophie Germain primes?

Cf. A005097, A005098, A124408, A124409, A124410, A124411, A071576.

[n: n in [0..1100] |IsPrime(2*n+1) and IsPrime(4*n+1)]; // Vincenzo Librandi, Apr 17 2013

Select[Range[1100], And @@ PrimeQ /@ ({2, 4}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)

is(k) = isprime(2*k+1) && isprime(4*k+1); \\ Jinyuan Wang, Aug 04 2019

Extended by Ray Chandler, Nov 20 2006

A124408 Numbers k such that 2k+1, 4k+1 and 6k+1 are primes.

Original entry on oeis.org

1, 3, 18, 105, 135, 153, 165, 168, 300, 363, 585, 618, 648, 765, 828, 1110, 1140, 1278, 1518, 1530, 1533, 2130, 2223, 2400, 2475, 2613, 2790, 2925, 3075, 3180, 3345, 3420, 3483, 3810, 3840, 3843, 3933, 4008, 4083, 4095, 4143, 4260, 4263, 4323, 4470, 4545

Offset: 1

Artur Jasinski, Oct 31 2006

nonn

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Cf. A005097, A005098, A024899, A123998, A124409, A124410, A124411, A071576.

Select[Range[4600], And @@ PrimeQ /@ ({2, 4, 6}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)

is(k) = sum(j = 1, 3, isprime(2*j*k+1)) == 3; \\ Jinyuan Wang, Aug 04 2019

A124410 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1 and 10k+1 are primes.

Original entry on oeis.org

5415, 12705, 13020, 44370, 82950, 98280, 105525, 112200, 115140, 123855, 134250, 134460, 187740, 188745, 210165, 225705, 247170, 256410, 296310, 302085, 367875, 375645, 382890, 399585, 404040, 476340, 487830, 526845, 532095, 566430, 578085

Offset: 1

Artur Jasinski, Oct 31 2006

nonn

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Cf. A005097, A005098, A024899, A005123, A024912, A123998, A124408, A124409, A124411, A071576.

Select[Range[600000], And @@ PrimeQ /@ ({2, 4, 6, 8, 10}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)

is(k) = sum(j = 1, 5, isprime(2*j*k+1)) == 5; \\ Jinyuan Wang, Aug 04 2019

A124411 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1, 10k+1 and 12k+1 are primes.

Original entry on oeis.org

12705, 13020, 105525, 256410, 966840, 1707510, 1944495, 2310000, 2478630, 3132675, 3836070, 3976770, 4112430, 4532325, 5499585, 5920005, 6610485, 7390845, 8552250, 10739505, 11120340, 12231450, 12338130, 13243230, 16467255

Offset: 1

Artur Jasinski, Oct 31 2006

nonn

Jinyuan Wang, Table of n, a(n) for n = 1..100

Cf. A005097, A005098, A024899, A005123, A024912, A110801, A123998, A124408, A124409, A124410, A071576.

Select[Range[10^7], And @@ PrimeQ /@ ({2, 4, 6, 8, 10, 12}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)

is(k) = sum(j = 1, 6, isprime(2*j*k+1)) == 6; \\ Jinyuan Wang, Aug 04 2019

Extended by Ray Chandler, Nov 20 2006

A237189 Numbers k such that k+1, 2k+1, 3k+1, 4k+1 are all prime.

Original entry on oeis.org

330, 1530, 3060, 4260, 4950, 6840, 10830, 15390, 18120, 23010, 25410, 26040, 31770, 33300, 40110, 41490, 45060, 49830, 53880, 59340, 65850, 70140, 73770, 78540, 88740, 95460, 96930, 109470, 111720, 112620, 117720, 131310, 133200, 134730, 135300, 150150, 165900

Offset: 1

Alex Ratushnyak, Feb 04 2014

nonn

A subsequence of A064238.

All terms are divisible by 30, and b(n)=a(n)/30 begins: 11, 51, 102, 142, 165, 228, 361, 513, 604, 767, 847, 868, 1059, 1110, 1337, 1383, 1502, 1661, 1796, 1978, 2195, ...

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Giovanni Resta)

Cf. A088250, A064238, A105653, A124409.

import sympy
from sympy import isprime
for n in range(0,100000,2):
    if isprime(n+1) and isprime(2*n+1) and isprime(3*n+1) and isprime(4*n+1):
        print(str(n), end=',')

a(n) = 2*(A105653(n) + 1) = 2*A124409(n). - Hugo Pfoertner, May 03 2021

cp's OEIS Frontend

A123998 Numbers k such that 2k+1 and 4k+1 are primes.

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A124408 Numbers k such that 2k+1, 4k+1 and 6k+1 are primes.

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A124410 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1 and 10k+1 are primes.

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A124411 Numbers k such that 2k+1, 4k+1, 6k+1, 8k+1, 10k+1 and 12k+1 are primes.

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A237189 Numbers k such that k+1, 2k+1, 3k+1, 4k+1 are all prime.

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