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A343775 Primes that are neither of the form (c^q+1)/(c+1) and nor of the form (b^k-1)/(b-1) 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, non-Brazilian 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, p-1, 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^k-1)/(b-1) = A085104 (Brazilian primes).

Primes of the form (c^q+1)/(c+1) = A059055.

Primes of the form (b^k-1)/(b-1) and also (c^q+1)/(c+1): A002383 \ {3} is a subsequence, but, maybe the intersection (conjecture).

Primes of the form (b^k-1)/(b-1) but not (c^q+1)/(c+1) = A225148.

Primes of the form (c^q+1)/(c+1) but not (b^k-1)/(b-1) = A343774.

Primes neither of the form (c^q+1)/(c+1) nor (b^k-1)/(b-1) = 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

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Last modified September 22 13:15 EDT 2021. Contains 347607 sequences. (Running on oeis4.)