A278694 -id:A278694 - cp's OEIS frontend

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

Randy L. Ekl, Nov 26 2016

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.

			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.

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

Cf. A278694.

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

A279956 Primes p such that every suffix of the base-4 representation of p is either a prime or 1.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43, 53, 59, 61, 67, 71, 83, 101, 107, 131, 139, 151, 157, 181, 193, 197, 199, 211, 229, 251, 257, 263, 269, 293, 317, 449, 467, 523, 541, 571, 613, 619, 643, 709, 769, 773, 787, 797, 811, 821, 827, 829, 839, 907, 919, 967, 997, 1019, 1031, 1061

Offset: 1

Randy L. Ekl, Dec 23 2016

			107 is a term in the sequence, since 107_10=1223_4, and 223_4, 23_4 and 3_4 (43_10, 11_10, and 3_10) are all prime.

Indranil Ghosh, Table of n, a(n) for n = 1..807

Cf. A278454 for base 2, A278694 for base 3, A278698 for base 5, and A033664 for base 10.

Also, cf. A278699 for base 4, where the final suffix cannot be 1 (it must be a prime, i.e., 2 or 3).

cp's OEIS Frontend

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

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