A278454 Primes p such that every suffix of the binary representation of p is either a prime or 1.

3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43, 61, 67, 71, 83, 101, 107, 131, 139, 151, 157, 199, 211, 229, 257, 263, 269, 293, 317, 467, 523, 541, 613, 619, 643, 769, 829, 1031, 1061, 1091, 1163, 1181, 1223, 1637, 1667, 2053, 2131, 2179, 2311, 2341, 3079, 3109, 3229, 3271, 4099, 4133, 4139, 4157, 4253, 4637, 8209, 8221, 8263, 8293, 8461, 9283, 9829, 9859

Offset: 1

Author

Randy L. Ekl, Nov 22 2016

Keywords

• nonn
• base

Examples

			211=11010011_2 is in the sequence, since each of its base-2 suffixes (1010011_2=83, 10011_2=19, 11_2=3, and 1_2=1) is either prime or 1.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A278455.

Programs

Magma

/* generates b-file through a(1027)=1770887435474165579843 in a couple of seconds */ /* Note: A[j] is a(j-1) */ A:=[1]; for d in [1..70] do for j in [1..#A] do t:=2^d+A[j]; if IsPrime(t) then A[#A+1]:=t; #A-1, A[#A]; end if; end for; end for; // Jon E. Schoenfield, Nov 23 2016

Mathematica

First /@ DeleteCases[Map[NestWhileList[# - 2^Floor@ Log2@ # &, #, # > 1 &] &, Prime@ Range[2, 1250]], w_ /; Times @@ Boole[PrimeQ /@ Most@ w] != 1] (* Michael De Vlieger, Nov 22 2016 *)

PARI

red(n)=n-(1<Joerg Arndt, Nov 23 2016