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

1,1

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

Links

Zak Seidov, Table of n, a(n) for n = 1..6000

R. J. Mathar, Table of Prime Gap Constellations

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A343085 A343968 A343969 * A298428 A252557 A237571

Adjacent sequences: A190814 A190815 A190816 * A190818 A190819 A190820

Keyword

nonn

Author

Zak Seidov, May 21 2011

Extensions

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

Status

approved