A190817 Initial primes of 6 consecutive primes with consecutive gaps 2,4,6,8,10.

13901, 21557, 28277, 55661, 68897, 128981, 221717, 354371, 548831, 665111, 954257, 1164587, 1246367, 1265081, 1538081, 1595051, 1634441, 2200811, 2798921, 2858621, 3053747, 3407081, 3414011, 3967487, 3992201, 4480241, 4608281, 4701731, 4809251, 5029457

Offset: 1

Author

Zak Seidov, May 21 2011

Keywords

• nonn

Comments

a(1) = 13901 = A190814(5) = A187058(7) = A078847(24).

a(n) + 30 is the greatest term in the sequence of 6 consecutive primes with consecutive gaps 2, 4, 6, 8, 10. - Muniru A Asiru, Aug 10 2017

Examples

			For n = 1, 13901 is in the sequence because 13901, 13903, 13907, 13913, 13921, 13931 are consecutive primes and for n = 2, 21557 is in the sequence since 21557, 21559, 21563, 21569, 21577, 21587 are consecutive primes. - _Muniru A Asiru_, Aug 24 2017
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..6000
• R. J. Mathar, Table of Prime Gap Constellations

Crossrefs

Cf. A078847, A187058, A190814, A190819, A190838.

Programs

GAP

K:=3*10^7+1;; # to get all terms <= K.
P:=Filtered([1,3..K],IsPrime);; I:=[2,4,6,8,10];;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4]]);;
P3:=List(Positions(P2,I),i->P[i]);  # Muniru A Asiru, Aug 24 2017

Maple

N:=10^7: # to get all terms <= N.
Primes:=select(isprime,[seq(i,i=3..N+30,2)]):
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]]=[2,4,6,8,10], [$1..nops(Primes)-5])]; # Muniru A Asiru, Aug 04 2017

Mathematica

d = Differences[Prime[Range[100000]]]; Prime[Flatten[Position[Partition[d, 5, 1], {2, 4, 6, 8, 10}]]] (* T. D. Noe, May 23 2011 *)
With[{s = Differences@ Prime@ Range[10^6]}, Prime[SequencePosition[s, Range[2, 10, 2]][[All, 1]] ] ] (* Michael De Vlieger, Aug 16 2017 *)

PARI

lista(nn) = forprime(p=13901, nn, if(nextprime(p+1)==p+2 && nextprime(p+3)==p+6 && nextprime(p+7)==p+12 && nextprime(p+13)==p+20 && nextprime(p+21)==p+30, print1(p", "))); \\ Altug Alkan, Aug 16 2017

Extensions

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