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

%I A278454 #19 Sep 08 2022 08:46:18
%S A278454 3,5,7,11,13,17,19,23,29,37,43,61,67,71,83,101,107,131,139,151,157,
%T A278454 199,211,229,257,263,269,293,317,467,523,541,613,619,643,769,829,1031,
%U A278454 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
%N A278454 Primes p such that every suffix of the binary representation of p is either a prime or 1.
%H A278454 Jon E. Schoenfield, <a href="/A278454/b278454.txt">Table of n, a(n) for n = 1..10000</a>
%e A278454 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.
%t A278454 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 *)
%o A278454 (Magma)
%o A278454 /* 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
%o A278454 (PARI)
%o A278454 red(n)=n-(1<<logint(n,2));
%o A278454 isok(n)=if(n==1,1,my(r=red(n));isprime(n)&&isok(red(n)));
%o A278454 forprime (p=3, 10^3,if(isok(p),print1(p,", ")));
%o A278454 \\ _Joerg Arndt_, Nov 23 2016
%Y A278454 Cf. A278455.
%K A278454 nonn,base
%O A278454 1,1
%A A278454 _Randy L. Ekl_, Nov 22 2016