A278696 Primes p such that every suffix of the ternary (base-3) representation of p is a prime.

2, 5, 11, 23, 29, 59, 83, 167, 173, 191, 491, 509, 569, 653, 659, 677, 1481, 1487, 1949, 2027, 2111, 4397, 4457, 4547, 4943, 5051, 5861, 6323, 6563, 13127, 13151, 13313, 13613, 13691, 13781, 13799, 15149, 15233, 17519, 17579, 17669, 39371, 39857, 40847, 40853, 43913, 44417, 52517, 53147, 59051

Offset: 1

Author

Randy L. Ekl, Nov 26 2016

Keywords

• nonn
• base

Comments

All numbers in the sequence are of one of the forms, base 3:

a. 2

b. 10...02, where there are 0 or more 0's

c. 20...0x, where there are 0 or more 0's, and x is of the form b or c

There is always exactly one 1 in the number, base 3.

All numbers end in a 2, base 3.

Examples

			569 is in the sequence, as 569=210002_3 and its base-3 suffixes are 10002_3=83 and 2_3=2, both of which are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A278694.

Programs

Maple

F[1]:= [2]:
for m from 2 to 11 do
  F[m]:= [op(F[m-1]),op(select(isprime, [seq(seq(i*3^
(m-1)+x,x=F[m-1]),i=[1,2])]))]
od:
F[11]; # Robert Israel, Jan 22 2020