A190814 Initial primes of 5 consecutive primes with consecutive gaps 2, 4, 6, 8.

347, 1427, 2687, 4931, 13901, 21557, 23741, 27941, 28277, 31247, 32057, 33617, 45821, 55661, 55817, 68207, 68897, 91571, 128657, 128981, 167621, 179897, 193871, 205421, 221717, 234191, 239231, 258107, 258611, 259157, 278807, 302831, 305477, 348431, 354371

Offset: 1

Author

Zak Seidov, May 20 2011

Keywords

• nonn

Comments

All terms = {11,17} mod 30.

a(n) + 20 is the greatest term in the sequence of 5 consecutive primes with 4 consecutive gaps 2, 4, 6, 8. - Muniru A Asiru, Aug 03 2017

Examples

			Prime(69..73) = {347, 349, 353, 359, 367} and 349 - 347 = 2, 353 - 349 = 4, 359 - 353 = 6, 367 - 359 = 8.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..2000

Crossrefs

Subsequence of A190799, also subsequence of A078847.

Cf. A190792, A190817, A190819, A190838.

Programs

Maple

N:= 10^6: # to get all terms <= N
Primes:= select(isprime, [seq(i,i=3..N+20,2)]):
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]] = [2,4,6,8], [$1..nops(Primes)-4])]; # Robert Israel, Aug 03 2017

Mathematica

d = Differences[Prime[Range[100000]]]; Prime[Flatten[Position[Partition[d, 4, 1], {2, 4, 6, 8}]]] (* T. D. Noe, May 23 2011 *)
Select[Partition[Prime[Range[31000]],5,1],Differences[#]=={2,4,6,8}&][[All,1]] (* Harvey P. Dale, Jul 03 2020 *)

Extensions

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