A278699 Primes p such that every suffix of the base-4 representation of p is a prime.

2, 3, 7, 11, 19, 23, 43, 59, 67, 71, 83, 107, 131, 139, 151, 199, 211, 251, 263, 467, 523, 571, 619, 643, 787, 811, 827, 839, 907, 919, 967, 1019, 1031, 1091, 1163, 1223, 1667, 1811, 1931, 2131, 2179, 2311, 2887, 3067, 3079, 3083, 3203, 3271, 3323, 3539, 3643, 3691, 3911, 4091, 4099, 4139

Offset: 1

Author

Randy L. Ekl, Nov 26 2016

Keywords

• nonn
• base

Comments

All numbers in the sequence are of the form 4n+3, except the number 2.

Examples

			23 is in the sequence, since 23 is prime, and the suffixes of 23 (113 base 4), 13 base 4 (7 base 10) and 3, are all prime.
		

Programs

Mathematica

With[{b = 4}, Select[Prime@ Range[10^3], Function[k, Times @@ Boole@ Map[PrimeQ@ FromDigits[Take[k, -#], b] &, Range[Length@ k - 1]] == 1]@ IntegerDigits[#, b] &]] (* Michael De Vlieger, Dec 01 2016 *)