A141898 -id:A141898 - 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,

A161504 Primes congruent to {1, 2, 10, 11, 19, 20} mod 21.

Original entry on oeis.org

2, 11, 19, 23, 31, 41, 43, 53, 61, 73, 83, 103, 107, 127, 137, 149, 157, 167, 179, 191, 199, 211, 229, 233, 241, 251, 263, 271, 283, 293, 313, 317, 337, 347, 359, 367, 379, 389, 397, 401, 409, 419, 421, 431, 439, 443, 461, 463, 503, 523, 547, 557, 569, 577, 587

Offset: 1

T. D. Noe, Jun 17 2009

nonn

The cyclotomic polynomial Phi(21p,x) is flat only for p in this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1001 [a(1)=2 inserted by _Georg Fischer_, Jul 26 2020]

Cf. A117223, A124826, A141888, A141892, A141893, A141897, A141898, A160495.

Flatten[Table[Select[21*n+{-10,-2,-1,1,2,10}, PrimeQ], {n,50}]]
Select[Prime[Range[2,250]],MemberQ[{1,2,10,11,19,20},Mod[#,21]]&] (* Harvey P. Dale, May 03 2019 *)

Union of A124826, A141888, A141892, A141893, A141897, A141898.

a(1)=2 inserted by Georg Fischer, Jul 26 2020

cp's OEIS Frontend

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

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