A290706 Greatest of 4 consecutive primes with consecutive gaps 2, 4, 6.

29, 53, 239, 359, 653, 1103, 1289, 1439, 1499, 1619, 2699, 3539, 3929, 4013, 4139, 4649, 4799, 4943, 8243, 9473, 10343, 11789, 12119, 13913, 14639, 20759, 21569, 23753, 25589, 26693, 26723, 27749, 27953, 28289, 29033, 31259

Offset: 1

Author

Muniru A Asiru, Aug 09 2017

Keywords

• nonn

Comments

All terms = {23, 29} mod 30.

Examples

			29 is a member of the sequence because 29 is the greatest of the 4 consecutive primes 17, 19, 23, 29 with consecutive gaps 2, 4, 6.
		

Crossrefs

Cf. A006512, A078847, A098412.

Programs

GAP

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

Maple

for i from 1 to 10^5 do if ithprime(i+1)=ithprime(i)+2 and ithprime(i+2)=ithprime(i)+6 and ithprime(i+3)=ithprime(i)+12 then print(ithprime(i+3)); fi; od;

Mathematica

Select[Prime@ Range@ 3500, NextPrime[#, {1, 2, 3}] == # + {2, 6, 12} &] + 12 (* Giovanni Resta, Aug 09 2017 *)

Formula

a(n) = A078847(n) + 12.