A372189 -id:A372189

Search: a372189 -id:a372189

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A126797

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

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..12.

Ken Nakamula, Hirofumi Tsumura, and Hiroaki Komai, New polynomials producing absolute pseudoprimes with any number of prime factors, arXiv:math/0702410 [math.NT], 2007. See Table 2, p. 9.

CROSSREFS

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

KEYWORD

nonn,more

AUTHOR

Jonathan Vos Post, Feb 20 2007

EXTENSIONS

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

STATUS

approved

A372186

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

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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, ...

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Ken Nakamula, Hirofumi Tsumura, and Hiroaki Komai, New polynomials producing absolute pseudoprimes with any number of prime factors, arXiv:math/0702410 [math.NT], 2007.

EXAMPLE

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.

MATHEMATICA

q[n_] := AllTrue[{20, 80, 100, 200}, PrimeQ[# * n + 1] &]; Select[Range[40000], q]

PROG

(PARI) is(n) = isprime(20*n + 1) && isprime(80*n + 1) && isprime(100*n + 1) && isprime(200*n + 1);

CROSSREFS

Cf. A002997, A318646, A372189.

Similar sequences: A046025, A257035, A206024, A206349, A372187, A372188.

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Apr 21 2024

STATUS

approved

A372190

Number of terms of A372188 that do not exceed 10^n.

+10
3

1, 2, 10, 33, 149, 824, 5116, 32077, 213075, 1463213, 10397977, 75903023

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..12.

Ken Nakamula, Hirofumi Tsumura, and Hiroaki Komai, New polynomials producing absolute pseudoprimes with any number of prime factors, arXiv:math/0702410 [math.NT], 2007. See Table 3, p. 9.

CROSSREFS

Cf. A002997, A036060, A126797, A372188, A372189.

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Apr 21 2024

STATUS

approved

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