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 1-4 of 4 results.

A206024 Numbers k such that 6k+1, 12k+1, 18k+1 and 36k+1 are all primes.

Original entry on oeis.org

1, 45, 56, 121, 206, 255, 380, 506, 511, 710, 871, 1025, 1421, 1515, 1696, 2191, 2571, 2656, 2681, 3341, 3566, 3741, 3796, 3916, 3976, 4235, 4340, 4426, 5645, 5875, 6006, 7066, 7616, 7826, 7976, 8900, 8925, 8976, 9025, 9186, 9600, 9761, 10920, 11301, 11385
Offset: 1

Views

Author

José María Grau Ribas, Feb 03 2012

Keywords

Comments

(6k+1)*(12k+1)*(18k+1)*(36k+1) is a Carmichael number for all k in this sequence. - José María Grau Ribas, Feb 06 2012

Links

Crossrefs

Cf. A002997, A046025, A206349, A257035.

Programs

  • GAP
    Filtered([1..12000],n->IsPrime(6*n+1) and IsPrime(12*n+1) and IsPrime(18*n+1) and IsPrime(36*n+1)); # Muniru A Asiru, May 27 2018
  • Magma
    [n: n in [0..2*10^4] | IsPrime(6*n+1) and IsPrime(12*n+1) and IsPrime(18*n+1) and  IsPrime(36*n+1)]; // Vincenzo Librandi, Apr 15 2015
  • Maple
    select(n->isprime(6*n+1) and isprime(12*n+1) and isprime(18*n+1) and isprime(36*n+1),[$1..12000]); # Muniru A Asiru, May 27 2018
  • Mathematica
    Select[Range[20000], PrimeQ[6 # + 1] && PrimeQ[12 # + 1] && PrimeQ[18 # + 1] && PrimeQ[36 # + 1] &]
Select[Range[12000],And@@PrimeQ[{6,12,18,36}#+1]&] (* Harvey P. Dale, Mar 25 2013 *)
  • PARI
    forprime(p=2,1e5,if(p%6!=1,next);if(isprime(2*p-1)&&isprime(3*p-2)&&isprime(6*p-5),print1(p\6", "))) \\ Charles R Greathouse IV, Feb 06 2012
  • PARI
    is(m,c=36)=!until(bittest(c\=2,0)&&9>c+=3, isprime(m*c+1)||return) \\ M. F. Hasler, Apr 15 2015

A372188 Numbers m such that 18*m + 1, 36*m + 1, 108*m + 1, and 162*m + 1 are all primes.

Original entry on oeis.org

1, 71, 155, 176, 241, 346, 420, 540, 690, 801, 1145, 1421, 1506, 2026, 2066, 3080, 3235, 3371, 3445, 3511, 3640, 4746, 4925, 5681, 5901, 6055, 6520, 7931, 8365, 8970, 9006, 9556, 9685, 10186, 11396, 11750, 11935, 12055, 12666, 13205, 13266, 13825, 13881, 14606
Offset: 1

Views

Author

Amiram Eldar, Apr 21 2024

Keywords

Comments

If m is a term, then (18*m + 1) * (36*m + 1) * (108*m + 1) * (162*m + 1) is a Carmichael number (A002997). These are the Carmichael numbers of the form W_4(3*m) in Nakamula et al. (2007).
The corresponding Carmichael numbers are 12490201, 288503529142321, 6548129556412321, ...

Examples

			1 is a term since 18*1 + 1 = 19, 36*1 + 1 = 37, 108*1 + 1 = 109, and 162*1 + 1 = 163 are all primes.
71 is a term since 18*71 + 1 = 1279, 36*71 + 1 = 2557, 108*71 + 1 = 7669, and 162*71 + 1 = 11503 are all primes.

Links

Crossrefs

Cf. A002997, A318646, A372190.
Similar sequences: A046025, A257035, A206024, A206349, A372186, A372187.

Programs

  • Mathematica
    q[n_] := AllTrue[{18, 36, 108, 162}, PrimeQ[#*n + 1] &]; Select[Range[15000], q]
  • PARI
    is(n) = isprime(18*n + 1) && isprime(36*n + 1) && isprime(108*n + 1) && isprime(162*n + 1);

A372186 Numbers m such that 20*m + 1, 80*m + 1, 100*m + 1, and 200*m + 1 are all primes.

Original entry on oeis.org

333, 741, 1659, 1749, 2505, 2706, 2730, 4221, 4437, 4851, 5625, 6447, 7791, 7977, 8229, 8250, 9216, 10833, 12471, 13950, 14028, 15147, 16002, 17667, 18207, 18246, 19152, 20517, 23400, 23421, 23961, 25689, 26247, 28587, 28608, 30363, 31584, 34167, 36330, 36378
Offset: 1

Views

Author

Amiram Eldar, Apr 21 2024

Keywords

Comments

If m is a term, then (20*m + 1) * (80*m + 1) * (100*m + 1) * (200*m + 1) is a Carmichael number (A002997). These are the Carmichael numbers of the form U_{4,4}(m) in Nakamula et al. (2007).
The corresponding Carmichael numbers are 393575432565765601, 9648687289456956001, 242412946401534283201, ...

Examples

			333 is a term since 20*333 + 1 = 6661, 80*333 + 1 = 26641, 100*333 + 1 = 33301, and 200*333 + 1 = 66601 are all primes.

Links

Crossrefs

Cf. A002997, A318646, A372189.
Similar sequences: A046025, A257035, A206024, A206349, A372187, A372188.

Programs

  • Mathematica
    q[n_] := AllTrue[{20, 80, 100, 200}, PrimeQ[# * n + 1] &]; Select[Range[40000], q]
  • PARI
    is(n) = isprime(20*n + 1) && isprime(80*n + 1) && isprime(100*n + 1) && isprime(200*n + 1);

A372187 Numbers m such that 72*m + 1, 576*m + 1, 648*m + 1, 1296*m + 1, and 2592*m + 1 are all primes.

Original entry on oeis.org

95, 890, 3635, 8150, 9850, 12740, 13805, 18715, 22590, 23591, 32526, 36395, 38571, 49016, 49456, 57551, 58296, 61275, 80756, 81050, 84980, 99940, 104346, 115361, 116761, 121055, 122550, 129320, 140331, 142625, 149431, 153505, 159306, 159730, 169625, 173485, 181661
Offset: 1

Views

Author

Amiram Eldar, Apr 21 2024

Keywords

Comments

If m is a term, then (72*m + 1) * (576*m + 1) * (648*m + 1) * (1296*m + 1) * (2592*m + 1) is a Carmichael number (A002997). These are the Carmichael numbers of the form U_{5,5}(m) in Nakamula et al. (2007).
The corresponding Carmichael numbers are 698669495582067436250881, 50411423376758357271937215361, 57292035175893741987253427965441, ...

Examples

			95 is a term since 72*95 + 1 = 6841, 576*95 + 1 = 54721, 648*95 + 1 = 61561, 1296*95 + 1 = 123121, and 2592*95 + 1 = 246241 are all primes.

Links

Crossrefs

Cf. A002997, A126797, A318646.
Similar sequences: A046025, A257035, A206024, A206349, A372186, A372188.

Programs

  • Mathematica
    q[n_] := AllTrue[{72, 576, 648, 1296, 2592}, PrimeQ[#*n + 1] &]; Select[Range[200000], q]
  • PARI
    is(n) = isprime(72*n + 1) && isprime(576*n + 1) && isprime(648*n + 1) && isprime(1296*n + 1) && isprime(2592*n + 1);
Showing 1-4 of 4 results.

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