A263770 -id:A263770 - cp's OEIS frontend

A263729 Primes p where (p - 1)/k - 1 is not prime for any integer k >= 1.

2, 3, 11, 23, 47, 59, 83, 107, 131, 167, 179, 227, 251, 263, 347, 359, 383, 431, 443, 467, 479, 503, 563, 587, 599, 719, 839, 863, 887, 947, 983, 1019, 1031, 1091, 1187, 1223, 1283, 1307, 1319, 1367, 1439, 1451, 1487

Offset: 1

Juri-Stepan Gerasimov, Oct 24 2015

Primes p such that (p^2 + p*q)/(p + 1) is not integer for all primes q.

Primes p such that d1 - 1, d2 - 1, .. are not primes where d1, d2, .. are all divisors of p - 1.

			11 is in this sequence because (11 - 1)/1 - 1 = 9, (11 - 1)/2 - 1 = 4, (11 - 1)/5 - 1 = 1, (11 - 1)/10 - 1 = 0 are nonprimes and 11 is prime.

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

Cf. A027750, A263730, A263770.

lista(nn) = {forprime (p=2, nn, ok = 1; for (k=1, p-1, x = (p-1)/k - 1; if (denominator(x)==1 && isprime(x), ok = 0; break);); if (ok, print1(p, ", ")););} \\ Michel Marcus, Nov 02 2015

Name edited by Franklin T. Adams-Watters, Oct 31 2015

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

A263729 Primes p where (p - 1)/k - 1 is not prime for any integer k >= 1.

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