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A190817
Initial primes of 6 consecutive primes with consecutive gaps 2,4,6,8,10.
12
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
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
KEYWORD
nonn
AUTHOR
Zak Seidov, May 21 2011
EXTENSIONS
Additional cross references from Harvey P. Dale, May 10 2014
STATUS
approved