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A341864 Least increasing sequence of primes a(n) == A020652(n) (mod A038567(n)).

%I A341864 #9 Feb 23 2021 05:28:48
%S A341864 3,7,11,13,19,31,37,43,59,61,71,113,149,157,179,229,251,257,283,293,
%T A341864 311,379,389,409,419,421,431,461,463,467,479,617,673,751,829,863,919,
%U A341864 953,1009,1021,1033,1069,1097,1123,1151,1171,1237,1277,1291,1409,1423,1489,1607,1621,1973,1987,2027,2087
%N A341864 Least increasing sequence of primes a(n) == A020652(n) (mod A038567(n)).
%C A341864 A020652/A038567 is an enumeration of the fractions < 1 (in lowest terms) arranged by increasing denominator and then increasing numerator.
%C A341864 a(n) is the least prime > a(n-1) congruent to A020652(n) (mod A038567(n)).
%H A341864 Robert Israel, <a href="/A341864/b341864.txt">Table of n, a(n) for n = 1..10000</a>
%e A341864 a(5) = 19 == A020652(5) = 3 (mod A038567(5) = 4) and is the least prime > a(4) = 13 with this property.
%p A341864 N:= 100: # for a(1)..a(N)
%p A341864 A:=Vector(N): A[1]:= 3: n:= 1:
%p A341864 for d from 3 while n < N do
%p A341864   for m from 1 to d-1 while n < N do
%p A341864     if igcd(m,d)=1 then
%p A341864       n:= n+1;
%p A341864       for k from ceil((A[n-1]+1 - m)/d) do
%p A341864         q:= d*k+m;
%p A341864         if isprime(q) then A[n]:= q; break fi
%p A341864       od
%p A341864     fi
%p A341864 od od:
%p A341864 convert(A,list);
%Y A341864 Cf. A020652, A038567.
%K A341864 nonn
%O A341864 1,1
%A A341864 _J. M. Bergot_ and _Robert Israel_, Feb 22 2021