A142068 -id:A142068 - cp's OEIS frontend

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

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,

A142066 Primes congruent to 29 mod 33.

Original entry on oeis.org

29, 227, 293, 359, 491, 557, 821, 887, 953, 1019, 1151, 1217, 1283, 1481, 1613, 1811, 1877, 2141, 2207, 2273, 2339, 2801, 2999, 3329, 3461, 3527, 3593, 3659, 3923, 3989, 4253, 4451, 4517, 4583, 4649, 5309, 5441, 5507, 5573, 5639, 5903, 6101, 6299, 6563

Offset: 1

N. J. A. Sloane, Jul 11 2008

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

Cf. A000040, A142067, A142068.

[p: p in PrimesUpTo(8000) | p mod 33 eq 29 ]; // Vincenzo Librandi, Aug 18 2012

Select[Range[29, 20000, 33], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jun 24 2011 *)
Select[Prime[Range[3000]],MemberQ[{29},Mod[#,33]]&] (* Vincenzo Librandi, Aug 18 2012 *)

is(n)=isprime(n) && n%33==29 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 20n log n. - Charles R Greathouse IV, Jul 03 2016

A161505 Primes congruent to {1, 7, 8, 25, 26, 32} mod 33.

Original entry on oeis.org

7, 41, 59, 67, 73, 107, 131, 139, 157, 173, 191, 197, 199, 223, 239, 257, 263, 271, 331, 337, 389, 397, 421, 461, 463, 487, 503, 521, 569, 587, 593, 601, 619, 653, 659, 661, 701, 719, 727, 733, 751, 857, 859, 883, 983, 991, 997, 1031, 1049, 1063, 1097, 1123

Offset: 1

T. D. Noe, Jun 17 2009

nonn

The cyclotomic polynomial Phi(33p,x) is flat only for p in this sequence.

Georg Fischer, Table of n, a(n) for n = 1..1000

Cf. A117223, A142049, A142053, A142054, A142063, A142064, A142068, A160495.

Flatten[Table[Select[33*n+{-8,-7,-1,1,7,8}, PrimeQ], {n,50}]]

Union of A142049, A142053, A142054, A142063, A142064, A142068.

a(1)=7 inserted by Georg Fischer, Jul 26 2020

A301619 Primes congruent to 65 (mod 192).

Original entry on oeis.org

257, 449, 641, 1217, 1409, 1601, 2753, 3137, 3329, 4289, 4481, 4673, 5441, 6977, 7937, 8513, 9281, 9473, 9857, 10433, 11393, 11777, 11969, 12161, 13121, 13313, 13697, 14081, 14657, 15233, 15809, 16001, 16193, 17729, 17921, 19073, 19457, 19841, 21377, 21569

Offset: 1

Felix Fröhlich, Mar 24 2018

In other words, primes of the form 192*k+65 for k > 0.

R. Scott and R. Styer, On p^x - q^y = c and related three term exponential Diophantine equations with prime bases, Journal of Number Theory, Vol. 105, No. 2 (2004), 212-234. See p. 218.

Subsequence of A002144 (primes of form 4*k+65) and A007519 (primes of form 8*k+65).

Cf. primes congruent to 65 (mod k): A142068 (k=66), A142137 (k=74), A142221 (k=82), A142271 (k=86), A142369 (k=94), A142427 (k=98), A142485 (k=102), A142542 (k=106), A142670 (k=114), A142733 (k=118), A142802 (k=122), A142890 (k=126), A105129 (k=128).

[p: p in PrimesUpTo(25000) | p mod 192 in {65}]; // Vincenzo Librandi, Jan 04 2020

Select[Prime[Range[2500]], MemberQ[{65}, Mod[#, 192]] &] (* Vincenzo Librandi, Jan 04 2020 *)

forprime(p=1, 5e4, if(Mod(p, 192)==65, print1(p, ", ")))

cp's OEIS Frontend

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

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A142066 Primes congruent to 29 mod 33.

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A161505 Primes congruent to {1, 7, 8, 25, 26, 32} mod 33.

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A301619 Primes congruent to 65 (mod 192).

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