A156828 -id:A156828 - cp's OEIS frontend

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

Jaroslav Krizek, Jan 23 2010

nonn

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

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

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

Note that all three of A025584, A156828, A175073 are different sequences. - N. J. A. Sloane, Apr 10 2011

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

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 *)

A156829 a(1) = 2. a(n) = the smallest prime >= a(n-1) + 6.

Original entry on oeis.org

2, 11, 17, 23, 29, 37, 43, 53, 59, 67, 73, 79, 89, 97, 103, 109, 127, 137, 149, 157, 163, 173, 179, 191, 197, 211, 223, 229, 239, 251, 257, 263, 269, 277, 283, 293, 307, 313, 331, 337, 347, 353, 359, 367, 373, 379, 389, 397, 409, 419, 431, 439, 449, 457, 463

Offset: 1

Leroy Quet, Feb 16 2009

nonn

Cf. A156828.

p := 2: for n from 1 to 1000 do printf("%d,",p) ; p := nextprime(p+5) ; od: # R. J. Mathar, Feb 22 2009

NestList[NextPrime[# + 5] &, 2, 45] (* Zak Seidov, Feb 08 2015 *)

More terms from R. J. Mathar, Feb 22 2009

cp's OEIS Frontend

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

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