A290264 - OEIS

%I #12 Aug 04 2017 15:45:14

%S 32465047,37091581,146742847,239659891,245333251,272213797,1060690651,

%T 1541736811,2002738207,2480351677,2636566351,4421955007,6168859201,

%U 8158683037,10367633527,10623394321,11452116817,11691059641,11892876841,13551877831,15043908637

%N Initial primes of 9 consecutive primes with 8 consecutive gaps 16, 14, 12, 10, 8, 6, 4, 2.

%C All terms = {1,7} mod 30.

%C For initial primes of 7 consecutive primes with 6 consecutive gaps 12, 10, 8, 6, 4, 2 and 8 consecutive primes with 7 consecutive gaps 14, 12, 10, 8, 6, 4, 2 see A290161 and A290162 respectively.

%C a(6) > 250000000.

%e 32465047 is a member of this sequence because the 9 consecutive primes 32465047, 32465063, 32465077, 32465089, 32465099, 32465107, 32465113, 32465117, 32465119 have consecutive gaps 16, 14, 12, 10, 8, 6, 4, 2. That is, 32465047 + 16 = 32465063, 32465063 + 14 = 32465077, 32465077 + 12 = 32465089, 32465089 + 10 = 32465099, 32465099 + 8 = 32465107, 32465107 + 6 = 32465113, 32465113 + 4 = 32465117, 32465117 + 2 = 32465119.

%o (GAP)

%o P:=Filtered([1..50000000],IsPrime);;I:=Reversed([2,4,6,8,10,12,14,16]);;

%o P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;  Collected(last);;

%o P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4],P1[i+5],P1[i+6],P1[i+7]]);;

%o P3:=List(Positions(P2,I),i->P[i]); Length(P3);

%Y Cf. A078847, A190814, A190817, A190819, A190838, A290161, A290162.

%K nonn

%O 1,1

%A _Muniru A Asiru_, Jul 25 2017

%E a(6)-a(21) from _Giovanni Resta_, Jul 25 2017