A355727 First of four consecutive primes p, q, r, s where q*s == p (mod r).

47, 139, 167, 257, 421, 557, 587, 647, 1021, 1051, 1217, 1601, 1759, 2957, 3803, 3911, 4007, 4397, 4423, 4463, 5351, 5471, 6257, 6691, 6857, 6949, 7577, 8081, 9109, 9697, 10223, 10847, 11927, 12101, 12601, 12911, 13669, 13711, 13751, 14537, 14621, 16217, 16607, 16903, 17021, 17359, 17477, 17911

Offset

1,1

Comments

Prime(i) is a term if A001223(i+1)*A0001223(i+2) = A001223(i) + A001223(i+1).

Links

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

Example

a(3) = 167 is a term because 167, 173, 179, 181 are consecutive primes with 173*181 == 167 (mod 179).

Maple

p2:= 2: p3:= 3: p4:=5: count:= 0: R:= NULL:
while count < 100 do
  p1:= p2; p2:= p3; p3:= p4; p4:= nextprime(p4);
  if p2*p4 -p1 mod p3 = 0 then
    count:= count+1;
    R:= R, p1;
  fi;
od:
R;

Crossrefs

Cf. A001223.

Sequence in context: A288408 A095311 A005112 * A062637 A212374 A040984

Adjacent sequences: A355724 A355725 A355726 * A355728 A355729 A355730

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 15 2022

Status

approved