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

3, 7, 11, 13, 19, 31, 37, 43, 59, 61, 71, 113, 149, 157, 179, 229, 251, 257, 283, 293, 311, 379, 389, 409, 419, 421, 431, 461, 463, 467, 479, 617, 673, 751, 829, 863, 919, 953, 1009, 1021, 1033, 1069, 1097, 1123, 1151, 1171, 1237, 1277, 1291, 1409, 1423, 1489, 1607, 1621, 1973, 1987, 2027, 2087

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 22 2021

Keywords

• nonn

Comments

A020652/A038567 is an enumeration of the fractions < 1 (in lowest terms) arranged by increasing denominator and then increasing numerator.

a(n) is the least prime > a(n-1) congruent to A020652(n) (mod A038567(n)).

Examples

			a(5) = 19 == A020652(5) = 3 (mod A038567(5) = 4) and is the least prime > a(4) = 13 with this property.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020652, A038567.

Programs

Maple

N:= 100: # for a(1)..a(N)
A:=Vector(N): A[1]:= 3: n:= 1:
for d from 3 while n < N do
  for m from 1 to d-1 while n < N do
    if igcd(m,d)=1 then
      n:= n+1;
      for k from ceil((A[n-1]+1 - m)/d) do
        q:= d*k+m;
        if isprime(q) then A[n]:= q; break fi
      od
    fi
od od:
convert(A,list);