A105653 -id:A105653 - cp's OEIS frontend

A105652 Numbers k such that p1=2k+3, p2=4k+5 and p3=6k+7 are all prime.

0, 2, 17, 104, 134, 152, 164, 167, 299, 362, 584, 617, 647, 764, 827, 1109, 1139, 1277, 1517, 1529, 1532, 2129, 2222, 2399, 2474, 2612, 2789, 2924, 3074, 3179, 3344, 3419, 3482, 3809, 3839, 3842, 3932, 4007, 4082, 4094, 4142, 4259, 4262, 4322, 4469, 4544

Offset: 1

Zak Seidov, Apr 16 2005

nonn

Except for 0, all terms == 2 or 14 (mod 15). - Robert Israel, Jun 08 2018

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A005382, A005383, A105610, A105653 - A105657, A174734.

[n: n in [0..5000] | IsPrime(2*n+3) and IsPrime(4*n+5) and IsPrime(6*n+7)]; // Vincenzo Librandi, Nov 13 2010

select(k -> andmap(isprime, [2*k+3,4*k+5,6*k+7]), [0, seq(seq(15*i+j,j=[2,14]),i=0..1000)]); # Robert Israel, Jun 08 2018

a(n) = (A174734(n)-3)/2. - Robert Israel, Jun 08 2018

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

A105655 Numbers k such that p1=2k+3, p2=4k+5, p3=6k+7, p4=8k+9, p5=10k+11 and p6=12k+13 are all prime.

Original entry on oeis.org

12704, 13019, 105524, 256409, 966839, 1707509, 1944494, 2309999, 2478629, 3132674, 3836069, 3976769, 4112429, 4532324, 5499584, 5920004, 6610484, 7390844, 8552249, 10739504, 11120339, 12231449, 12338129, 13243229, 16467254

Offset: 1

Zak Seidov, Apr 16 2005

nonn

Cf. A005382, A005383, A105610, A105652, A105653, A105654, A105656, A105657.

[n: n in [0..10000000]|IsPrime(2*n+3) and IsPrime(4*n+5) and IsPrime(6*n+7) and IsPrime(8*n+9) and IsPrime(10*n+11)and IsPrime(12*n+13)] // Vincenzo Librandi, Dec 16 2010

With[{r1=Range[2,12,2],r2=Range[3,13,2]},Select[Range[16500000],And@@PrimeQ[# r1+r2]&]] (* Harvey P. Dale, Jan 31 2011 *)

cp's OEIS Frontend

A105652 Numbers k such that p1=2k+3, p2=4k+5 and p3=6k+7 are all prime.

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

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A105655 Numbers k such that p1=2k+3, p2=4k+5, p3=6k+7, p4=8k+9, p5=10k+11 and p6=12k+13 are all prime.

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