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A317851 Primes p such that A090086(p+1) < p. 1
31, 43, 61, 67, 73, 79, 97, 103, 107, 113, 127, 131, 137, 151, 163, 167, 173, 181, 191, 193, 197, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Theorem: if n-1 is composite, then A090086(n) < n.

The inverse theorem is false iff n = p+1 for primes p in this sequence.

Conjecture: the sequence contains all sufficiently large primes. Probably all primes except 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 47, 53, 59, 71, 83, 89, 101, 109, 139, 149, 157, 179, 199, 307, 461, and 571.

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

The prime 31 is a term, since A090086(31+1) = 25 < 31.

PROG

(PARI) b(n) = {forcomposite(k=2, , if (Mod(n, k)^(k-1) == 1, return (k)); ); }

isok(p) = isprime(p) && (b(p+1) < p); \\ Michel Marcus, Aug 09 2018

CROSSREFS

Cf. A000040, A090086.

Sequence in context: A089713 A281246 A067467 * A304239 A069455 A211549

Adjacent sequences:  A317848 A317849 A317850 * A317852 A317853 A317854

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Aug 09 2018

EXTENSIONS

Corrected and extended by Michel Marcus, Aug 09 2018

STATUS

approved

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Last modified June 21 04:10 EDT 2021. Contains 345354 sequences. (Running on oeis4.)