OFFSET
1,1
COMMENTS
Subsequence of A175071.
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 23 2010
STATUS
approved