A290264 Initial primes of 9 consecutive primes with 8 consecutive gaps 16, 14, 12, 10, 8, 6, 4, 2.

32465047, 37091581, 146742847, 239659891, 245333251, 272213797, 1060690651, 1541736811, 2002738207, 2480351677, 2636566351, 4421955007, 6168859201, 8158683037, 10367633527, 10623394321, 11452116817, 11691059641, 11892876841, 13551877831, 15043908637

Offset: 1

Author

Muniru A Asiru, Jul 25 2017

Keywords

• nonn

Comments

All terms = {1,7} mod 30.

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.

a(6) > 250000000.

Examples

			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.
		

Crossrefs

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

Programs

GAP

P:=Filtered([1..50000000],IsPrime);;I:=Reversed([2,4,6,8,10,12,14,16]);;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;  Collected(last);;
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]]);;
P3:=List(Positions(P2,I),i->P[i]); Length(P3);

Extensions

a(6)-a(21) from Giovanni Resta, Jul 25 2017