cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A067256 Numbers n such that n, 2n+1, 3n+2 are primes.

Original entry on oeis.org

3, 5, 23, 29, 83, 89, 173, 233, 239, 293, 419, 659, 953, 1013, 1223, 1409, 1559, 1583, 1889, 2003, 2129, 2339, 2549, 2693, 2939, 3359, 3389, 3593, 3803, 4349, 4373, 4409, 4919, 4943, 5333, 6113, 6173, 8093, 8273, 8513, 9059, 9479, 9539, 10163, 10313
Offset: 1

Views

Author

Benoit Cloitre, Feb 20 2002

Keywords

Comments

a(n)*(2a(n)+1)*(3a(n)+2) are Lucas-Carmichael numbers for n > 1. Analogous to A174734 as A006972 (Lucas-Carmichael numbers) is analogous to A002997 (Carmichael numbers). - Amiram Eldar, Aug 11 2017

Links

Crossrefs

Cf. A000040, A005384, A006972, A067257, A067258, A101767, A101768, A101769, A101770, A174734, A216925.

Programs

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

Original entry on oeis.org

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

Views

Author

Zak Seidov, Apr 16 2005

Keywords

Comments

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

Links

Crossrefs

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

Programs

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

Formula

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

A137702 Prime numbers p such that p +- ((p-1)/2) are primes.

Original entry on oeis.org

5, 13, 73, 421, 541, 613, 661, 673, 1201, 1453, 2341, 2473, 2593, 3061, 3313, 4441, 4561, 5113, 6073, 6121, 6133, 8521, 8893, 9601, 9901, 10453, 11161, 11701, 12301, 12721, 13381, 13681, 13933, 15241, 15361, 15373, 15733, 16033, 16333, 16381
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2008

Keywords

Examples

			(5-2, 5+2) are prime
(13-6, 13+6) are prime

Links

Crossrefs

Cf. A174734.

Programs

  • Mathematica
    Select[Prime[Range[1000]], PrimeQ[#-(#-1)/2] && PrimeQ[#+(#-1)/2]&]
  • PARI
    forprime(p=3,1e5,if(isprime(p+p\2)&isprime(p\2+1),print1(p", ")))

A180025 Prime numbers 3*n-2 such that n, 2*n-1 and 3*n-2 are prime.

Original entry on oeis.org

7, 19, 109, 631, 811, 919, 991, 1009, 1801, 2179, 3511, 3709, 3889, 4591, 4969, 6661, 6841, 7669, 9109, 9181, 9199, 12781, 13339, 14401, 14851, 15679, 16741, 17551, 18451, 19081, 20071, 20521, 20899, 22861, 23041, 23059, 23599, 24049, 24499
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2011

Keywords

Examples

			3.5.7, 7.13.19, 37.73.109, 211.421.631, 271.541.811 = A174734.A137702.A180025

Crossrefs

Cf. A137702, A174734

Programs

  • Mathematica
    Select[Prime[Range[1000]], PrimeQ[2*#-1] && PrimeQ[3*#-2]&]*3-2

A386540 Primes p such that 2p - 1, 3p - 2, (p + 1)/2, and (p + 2)/3 are also prime.

Original entry on oeis.org

37, 2557, 3061, 5581, 88741, 124021, 157081, 178537, 216217, 216757, 217057, 330661, 344821, 352081, 387577, 423481, 459397, 477577, 521137, 790861, 806521, 865957, 869521, 1369657, 1517881, 1673401, 1704397, 1710661, 1970257, 2132797, 2292781, 2361781, 2680141
Offset: 1

Views

Author

Holger Wallenta, Jul 25 2025

Keywords

Comments

All terms are congruent to 1 modulo 12.
Let q = (p + 1)/2 and r = (p + 2)/3; then 3r = 2q + 1.

Examples

			37 is a term, since it is prime and 2*37 - 1 = 73, 3*37 - 2 = 109, (37 + 1)/2 = 19 and (37 + 2)/3 = 13 are all prime.

Links

Crossrefs

Intersection of A036570 and A174734.

Programs

  • Maple
    select(p -> andmap(isprime,[p, 2*p-1,3*p-2,(p+1)/2,(p+2)/3]), [seq(1+12*i,i=1..10^6)]); # Robert Israel, Jul 25 2025
  • Mathematica
    Select[Prime[Range[2*10^5]],AllTrue[{2#-1,3#-2,(#+1)/2,(#+2)/3},PrimeQ]&] (* James C. McMahon, Jul 25 2025 *)
  • Python
    from gmpy2 import is_prime
def ok(p): return p&1 and p%3 == 1 and all(is_prime(q) for q in [p, 2*p-1, 3*p-2, (p+1)//2, (p+2)//3])
print([k for k in range(1, 10**7, 12) if ok(k)]) # Michael S. Branicky, Jul 25 2025
Showing 1-5 of 5 results.

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