A141926 -id:A141926 - cp's OEIS frontend

A141923 Primes congruent to 19 mod 23.

19, 157, 433, 479, 571, 617, 709, 1031, 1123, 1307, 1399, 1583, 1721, 1951, 1997, 2089, 2273, 2411, 2503, 2549, 2687, 2917, 2963, 3331, 3469, 3607, 3929, 4021, 4159, 4297, 4481, 4987, 5171, 5309, 5861, 5953, 6091, 6229, 6367, 6551, 6689, 6781, 6827, 7057

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141924, A141925, A141926.

[p: p in PrimesUpTo(9000) | p mod 23 eq 19 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[19,20000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 18 2011 *)
Select[Prime[Range[1000]],Mod[#,23]==19&] (* Harvey P. Dale, Jul 01 2023 *)

is(n)=isprime(n) && n%23==19 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 02 2016

A141924 Primes congruent to 20 mod 23.

Original entry on oeis.org

43, 89, 181, 227, 457, 503, 641, 733, 1009, 1193, 1423, 1607, 1699, 2113, 2251, 2297, 2389, 2711, 2803, 3079, 3217, 3539, 3631, 3677, 3769, 3907, 4091, 4229, 4597, 4643, 4919, 5011, 5333, 5471, 5563, 5701, 5839, 6299, 6529, 7127, 7219, 7541, 7817, 8093

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141925, A141926.

[p: p in PrimesUpTo(9000) | p mod 23 eq 20 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[20,20000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 18 2011 *)

is(n)=isprime(n) && n%23==20 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 02 2016

A141925 Primes congruent to 21 mod 23.

Original entry on oeis.org

67, 113, 251, 389, 619, 757, 941, 1033, 1171, 1217, 1447, 1493, 1723, 1861, 1907, 1999, 2137, 2459, 2551, 2689, 3011, 3517, 3701, 3793, 3931, 4253, 4391, 4483, 4621, 4759, 4943, 5081, 5449, 6047, 6277, 6323, 6553, 6599, 6691, 6737, 6829, 6967, 7013, 7151

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141926.

[p: p in PrimesUpTo(9000) | p mod 23 eq 21 ]; // Vincenzo Librandi, Aug 16 2012

Select[Range[21,20000,23],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 18 2011 *)

is(n)=isprime(n) && n%23==21 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 02 2016

A212374 Primes congruent to 1 mod 23.

Original entry on oeis.org

47, 139, 277, 461, 599, 691, 829, 967, 1013, 1151, 1289, 1381, 1427, 1657, 1933, 1979, 2347, 2393, 2531, 3037, 3083, 3221, 3313, 3359, 3727, 3911, 4003, 4049, 4463, 4831, 4877, 4969, 5107, 5153, 5521, 5659, 5843, 5981, 6073, 6211, 6257, 6763, 6947, 7039, 7177

Offset: 1

Bruno Berselli, Sep 12 2012

This sequence is not the same as A040984. First disagreement at index 34: a(34)=5153, A040984(34)=5521.

Bruno Berselli, Table of n, a(n) for n = 1..1000

Cf. A100201, A102734, A141908-A141926, A040984.

[p: p in PrimesUpTo(7200) | p mod 23 eq 1];

select(p->irem(p, 23)=1, [ithprime(i)$i=1..1000])[]; # Alois P. Heinz, Sep 12 2012

Select[Prime[Range[1000]], Mod[#, 23] == 1 &]
Select[Range[1,7200,23],PrimeQ] (* Harvey P. Dale, Jul 02 2018 *)

is(n)=isprime(n) && n%23==1 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 22n log n. - Charles R Greathouse IV, Jul 03 2016

A263769 Smallest prime q such that q == -1 (mod prime(n)-1).

Original entry on oeis.org

2, 3, 3, 5, 19, 11, 31, 17, 43, 83, 29, 71, 79, 41, 137, 103, 173, 59, 131, 139, 71, 233, 163, 263, 191, 199, 101, 211, 107, 223, 251, 389, 271, 137, 443, 149, 311, 647, 331, 859, 1423, 179, 379, 191, 587, 197, 419, 443

Offset: 1

Juri-Stepan Gerasimov, Oct 25 2015

nonn

a(n): A000040(1), A065091(1), A002145(1), A007528(1), A030433(1), A068231(1), A127576(1), A061242(1), A141857(1), A141976(1), A132236(1), A142111(1), A142198(1), A141898(1), A141926(1), A142531(1), A142004(1), A142799(1), A142068(1), A142099(1), ...

Smallest prime q such that (prime(n)^2 + q*prime(n))/(prime(n) + 1) is an integer.

			a(4) = 5 because 5 == -1 (mod prime(4)-1) and is prime.

Robert Israel, Table of n, a(n) for n = 1..6000

Cf. A263730, A263770.

Cf. A000040, A065091, A002145, A007528, A030433, A068231, A127576, A061242, A141857, A141976, A132236, A142111, A142198, A141898, A141926, A142531, A142004, A142799, A142068, A142099.

for n from 1 to 100 do
  k:= ithprime(n)-1;
  q:= 2;
  while (1 + q) mod k <> 0 do
    q:= nextprime(q)
  od;
  A[n]:= q;
od:
seq(A[i],i=1..1000); # Robert Israel, Oct 26 2015

Table[q = 2; z = Prime@ n - 1; While[Mod[q, z] != z - 1, q = NextPrime@ q]; q, {n, 59}] (* Michael De Vlieger, Oct 26 2015 *)

Corrected and edited by Robert Israel, Oct 26 2015,

cp's OEIS Frontend

A141923 Primes congruent to 19 mod 23.

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A141924 Primes congruent to 20 mod 23.

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A141925 Primes congruent to 21 mod 23.

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A212374 Primes congruent to 1 mod 23.

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A263769 Smallest prime q such that q == -1 (mod prime(n)-1).

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