A129901 For two consecutive primes p and q the difference 10*q - p is prime. The first of the pair of primes is listed.

3, 7, 13, 17, 19, 29, 37, 41, 67, 71, 79, 89, 101, 103, 107, 109, 149, 193, 227, 241, 269, 281, 283, 293, 307, 311, 313, 349, 389, 397, 421, 457, 479, 487, 547, 613, 617, 631, 643, 701, 709, 719, 739, 769, 829, 839, 853, 863, 877, 881, 1049, 1091, 1109, 1153

Offset

1,1

Comments

Both can't be the same form 3n+1 or 3n+2. Since the primes alternate very frequently between 3n+1, 3n+2, 3n+1... this sequence produces a decent frequency of primes.

Links

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

Example

For 19 and 23, 23*10 - 19 = 230-19 = 211, a prime.

Maple

R:= NULL: q:= 2: count:= 0:
while count < 100 do
  p:= q; q:= nextprime(q);
  if isprime(10*q-p) then count:= count+1; R:= R, p fi
od:
R; # Robert Israel, Jul 14 2020

Mathematica

a = {}; For[n=1, n<200, n++, If[PrimeQ[10*Prime[n+1]-Prime[n]], AppendTo[a, Prime[n]]]]; a (* Stefan Steinerberger, Jun 07 2007 *)

Crossrefs

Sequence in context: A290400 A040999 A172240 * A067073 A323579 A124273

Adjacent sequences: A129898 A129899 A129900 * A129902 A129903 A129904

Keyword

nonn

Author

J. M. Bergot, Jun 04 2007

Extensions

Corrected and extended by Stefan Steinerberger, Jun 07 2007

Status

approved