

A175073


Primes q with result 1 under iterations of {r mod (max prime p < r)} starting at r = q.


3



3, 11, 17, 23, 29, 37, 41, 47, 53, 59, 67, 71, 79, 83, 89, 97, 101, 107, 113, 127, 131, 137, 149, 157, 163, 167, 173, 179, 191, 197, 211, 223, 227, 233, 239, 251, 257, 263, 269, 277, 281, 293, 307
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OFFSET

1,1


COMMENTS

Subsequence of A175071.
Union of a(n) and A175074 is A175071.  Jaroslav Krizek, Jan 30 2010
The terms in A025584 but not in here are 2, 2999, 3299, 5147, 5981, 8999, 9587, ... , apparently those listed in A175080.  R. J. Mathar, Feb 01 2010
a(n1)=A156828(n) in the range n=3..348, but afterwards the sequences differ because numbers like 2999 and 3229 are in A156828 but not in here.  R. J. Mathar, Mar 01 2010
Conjecture: under this iteration procedure, all primes eventually will yield either a 2 or a 1. If a 2 results, all subsequent terms are zeros; if a 1 results, all subsequent terms are 1s. The conjecture is true for the first 2 million primes.  Harvey P. Dale, Jan 17 2014


LINKS

Table of n, a(n) for n=1..43.


EXAMPLE

Iteration procedure for a(2) = 11: 11 mod 7 = 4, 4 mod 3 = 1.


MATHEMATICA

r1Q[n_] := FixedPoint[Mod[#, NextPrime[#, 1]] &, n] == 1; Select[Prime[ Range[70]], r1Q] (* This program relies upon the conjecture described in the comments above *) (* Harvey P. Dale, Jan 17 2014 *)


CROSSREFS

Note that all three of A025584, A156828, A175073 are different sequences.  N. J. A. Sloane, Apr 10 2011
Sequence in context: A322962 A075334 A056983 * A062284 A141339 A069348
Adjacent sequences: A175070 A175071 A175072 * A175074 A175075 A175076


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Jan 23 2010


STATUS

approved



