A190838 Initial primes of 8 consecutive primes with 7 consecutive gaps 2, 4, 6, 8, 10, 12, 14.

128981, 21456047, 34864211, 51867197, 55793951, 69726647, 113575727, 180078317, 207664397, 232728647, 342241967, 382427027, 382533311, 470463011, 558791327, 591360851, 603413801, 749930717, 838115711, 926976431, 965761397, 1007421251, 1109867567, 1278189947

Offset: 1

Author

Zak Seidov, May 21 2011

Keywords

• nonn

Comments

a(1) = 128981 = A190819(1), a(2) = 21456047 = A190819(14).

a(n) + 56 is the greatest term in the sequence of 8 consecutive primes with 7 consecutive gaps 2, 4, 6, 8, 10, 12, 14. - Muniru A Asiru, Aug 10 2017

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index entries for primes, gaps between

Crossrefs

Subsequence of A190819.

Subsequence of A187060. - Michel Marcus, Aug 10 2017

Cf. A078847, A190814, A190817.

Programs

Maple

N:=10^8:  # to get all terms <= N.
Primes:=select(isprime,[seq(i,i=3..N+56,2)]):
Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1],
  Primes[t+3]-Primes[t+2], Primes[t+4]-Primes[t+3], Primes[t+5]-
  Primes[t+4], Primes[t+6]-Primes[t+5] , Primes[t+7]-Primes[t+6] ]=
[2,4,6,8,10,12,14], [$1..nops(Primes)-7])]; # Muniru A Asiru, Aug 04 2017

Mathematica

Transpose[Select[Partition[Prime[Range[65000000]],8,1],Differences[#] =={2,4,6,8,10,12,14}&]][[1]] (* Harvey P. Dale, May 10 2014 *)

PARI

list(lim)=my(v=List(),p=128981,t); forprime(q=p+2,lim+56, if(q-p-t==2, t+=2; if(t==14, listput(v, q-56); t=0), t=0); p=q); Vec(v) \\ Charles R Greathouse IV, Aug 10 2017

Extensions

Additional cross references from Harvey P. Dale, May 10 2014