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 1-3 of 3 results.

A126797 Number of terms of A372187 that do not exceed 10^n.

Original entry on oeis.org

0, 1, 2, 5, 22, 107, 616, 3516, 22163, 144739, 979292, 6803735
Offset: 1

Views

Author

Jonathan Vos Post, Feb 20 2007

Keywords

Links

Crossrefs

Cf. A002997, A036060, A372187, A372189, A372190.

Extensions

a(1)-a(2) prepended, a(10)-a(12) added, and name edited by Amiram Eldar, Apr 21 2024

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);
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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