A175073 Primes q with result 1 under iterations of {r mod (max prime p < r)} starting at r = q.

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

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(n-1)=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

R. J. Mathar, Table of n, a(n) for n = 1..10000

Example

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

Maple

isA175073 := proc(p)
    local r, rold;
    if not isprime(p) then
        return false;
    end if;
    r := p ;
    while true do
        rold :=r ;
        if r = 2 then
            return false ;
        end if;
        r := modp(r, prevprime(r)) ;
        if r = 1 then
            return true;
        elif r= rold then
            return false ;
        end if;
    end do:
end proc:
A175073 := proc(n)
    option remember ;
    if n= 1 then
        3;
    else
        for p from procname(n-1)+2 by 2 do
            if isA175073(p) then
                return p;
            end if;
        end do:
    end if;
end proc:
seq(A175073(n), n=1..40) ; # R. J. Mathar, Mar 25 2024

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