A054690 n consecutive primes differ by 4 or more starting at a(n), or n consecutive primes with no twin primes.

7, 19, 43, 73, 73, 349, 349, 349, 349, 349, 349, 661, 661, 661, 661, 661, 661, 661, 661, 8629, 8629, 8629, 8629, 13399, 13399, 13399, 14629, 14629, 24421, 24421, 24421, 24421, 24421, 24421, 24421, 24421, 24421, 24421, 24421, 24421, 24421

Offset: 2

Author

Jeff Burch, Apr 19 2000

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 2..204

Crossrefs

Cf. A054691, A054692.

Programs

Maple

P:= select(isprime, [seq(i,i=3..10^7,2)]):
A:= 'A':
state:= 0: smax := 0:
for i from 2 to nops(P) do
  if P[i] - P[i-1] >= 4 then
    state:= state + 1;
    if state > smax then smax:= state; A[state+1]:= P[i-state] fi
  else
    state:= 0;
  fi
od:
seq(A[i],i=2..smax+1); # Robert Israel, Jun 27 2017

Mathematica

Prime[#]&/@With[{pd=If[#>2,1,0]&/@Differences[Prime[Range[3000]]]}, Flatten[ Table[ SequencePosition[pd,PadRight[{},n,1],1][[All,1]],{n,45}]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 29 2018 *)