

A343775


Primes that are neither of the form (c^q+1)/(c+1) and nor of the form (b^k1)/(b1) for any b, c > 1 and k, q primes > 2.


1



2, 5, 17, 19, 23, 29, 37, 41, 47, 53, 59, 67, 71, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367
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OFFSET

1,1


COMMENTS

Equivalently, nonBrazilian primes that are not of the form (c^q+1)/(c+1) for some c > 1, q prime > 2.
Equals A220627 \ A059055.


LINKS

Table of n, a(n) for n=1..60.


PROG

(PARI) isc(p) = for (b=2, p, my(k=3); while ((x=(b^k+1)/(b+1)) <= p, if (x == p, return (1)); k = nextprime(k+1); ); );
isnotb(p) = for (b=2, p1, my(d=digits(p, b), md=vecmin(d)); if ((#d > 2) && (md == 1) && (vecmax(d) == 1), return (0)); ); return (1);
isok(p) = isprime(p) && !isc(p) && isnotb(p); \\ Michel Marcus, May 01 2021


CROSSREFS

Primes of the form (b^k1)/(b1) = A085104 (Brazilian primes).
Primes of the form (c^q+1)/(c+1) = A059055.
Primes of the form (b^k1)/(b1) and also (c^q+1)/(c+1): A002383 \ {3} is a subsequence, but, maybe the intersection (conjecture).
Primes of the form (b^k1)/(b1) but not (c^q+1)/(c+1) = A225148.
Primes of the form (c^q+1)/(c+1) but not (b^k1)/(b1) = A343774.
Primes neither of the form (c^q+1)/(c+1) nor (b^k1)/(b1) = this sequence.
Sequence in context: A123364 A247857 A025553 * A075544 A104247 A215425
Adjacent sequences: A343772 A343773 A343774 * A343776 A343777 A343778


KEYWORD

nonn,base


AUTHOR

Bernard Schott, Apr 29 2021


STATUS

approved



