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

1,1

Links

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

Example

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.

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 *)

Prog

(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
(PARI)
red(n)=n-(1<<logint(n, 2));
isok(n)=if(n==1, 1, my(r=red(n)); isprime(n)&&isok(red(n)));
forprime (p=3, 10^3, if(isok(p), print1(p, ", ")));
\\ Joerg Arndt, Nov 23 2016

Crossrefs

Cf. A278455.

Sequence in context: A226181 A363286 A120637 * A064534 A139758 A306084

Adjacent sequences: A278451 A278452 A278453 * A278455 A278456 A278457

Keyword

nonn,base

Author

Randy L. Ekl, Nov 22 2016

Status

approved