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

1,1

Comments

All terms = {23, 29} mod 30.

Links

Table of n, a(n) for n=1..36.

Formula

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

Example

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.

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 *)

Prog

(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)]);

Crossrefs

Cf. A006512, A078847, A098412.

Sequence in context: A243439 A216497 A139877 * A044081 A044462 A161714

Adjacent sequences: A290703 A290704 A290705 * A290707 A290708 A290709

Keyword

nonn

Author

Muniru A Asiru, Aug 09 2017

Status

approved