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A242755 Primes p such that pi(p)*q == 1 (mod p) for some prime q < p, where pi(p) is the number of primes not exceeding p. 5
3, 5, 7, 13, 17, 29, 31, 41, 59, 61, 73, 127, 157, 173, 179, 199, 223, 227, 239, 241, 271, 281, 311, 317, 349, 353, 359, 367, 379, 419, 439, 479, 487, 503, 541, 557, 599, 643, 653, 709, 769, 773, 809, 823, 829, 839, 859, 941, 953, 1063 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
According to the conjecture in A242753, this sequence should contain infinitely many primes.
Conjecture: The number of such primes not exceeding x > 1 has the main term x/(log x)^2 as x tends to infinity.
LINKS
EXAMPLE
a(4) = 13 since 13 is prime with pi(13) = 6, and 6*11 == 1 (mod 13) with 11 prime, but pi(11)*9 == 1 (mod 11) with 9 not prime.
MATHEMATICA
p[n_]:=PrimeQ[PowerMod[n, -1, Prime[n]]]
n=0; Do[If[p[k], n=n+1; Print[n, " ", Prime[k]]]; Continue, {k, 1, 179}]
CROSSREFS
Sequence in context: A177070 A247018 A038929 * A070806 A339506 A178490
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 22 2014
STATUS
approved

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Last modified March 29 08:47 EDT 2024. Contains 371267 sequences. (Running on oeis4.)