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Primes p where (p - 1)/k - 1 is not prime for any integer k >= 1.
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%I #30 Nov 25 2019 03:31:05

%S 2,3,11,23,47,59,83,107,131,167,179,227,251,263,347,359,383,431,443,

%T 467,479,503,563,587,599,719,839,863,887,947,983,1019,1031,1091,1187,

%U 1223,1283,1307,1319,1367,1439,1451,1487

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

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

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

%H Amiram Eldar, <a href="/A263729/b263729.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%o (PARI) 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

%Y Cf. A027750, A263730, A263770.

%K nonn,easy

%O 1,1

%A _Juri-Stepan Gerasimov_, Oct 24 2015

%E Name edited by _Franklin T. Adams-Watters_, Oct 31 2015