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A329877 Lexicographically earliest sequence of positive integers such that for n > 1, the concatenation of a(n), a(n-1), ..., a(1), in binary, is a prime number.

%I A329877 #7 Nov 23 2019 13:21:20
%S A329877 1,1,1,2,4,3,7,10,18,1,13,5,2,42,3,3,22,18,23,15,29,33,23,17,5,33,3,
%T A329877 134,94,84,6,57,103,13,92,63,90,60,156,39,10,108,114,65,78,67,52,57,
%U A329877 11,21,114,79,366,128,76,22,382,36,88,34,68,110,2,72,14,28
%N A329877 Lexicographically earliest sequence of positive integers such that for n > 1, the concatenation of a(n), a(n-1), ..., a(1), in binary, is a prime number.
%C A329877 This sequence is a binary variant of A329876.
%C A329877 For any n > 0, the binary concatenation of a(n+1) and A329875(n) gives A329875(n+1).
%e A329877 The first terms, alongside their binary representations and the corresponding concatenations, are:
%e A329877   n   a(n)  bin(a(n))  bin(A329875(n))
%e A329877   --  ----  ---------  -----------------------
%e A329877    1     1          1                        1
%e A329877    2     1          1                       11
%e A329877    3     1          1                      111
%e A329877    4     2         10                    10111
%e A329877    5     4        100                 10010111
%e A329877    6     3         11               1110010111
%e A329877    7     7        111            1111110010111
%e A329877    8    10       1010        10101111110010111
%e A329877    9    18      10010   1001010101111110010111
%e A329877   10     1          1  11001010101111110010111
%o A329877 (PARI) print1 (v=1); for (n=2, 69, s=(b=2)^#digits(v, b); for (k=1, oo, if (isprime(v+=s), print1 (", "k); break)))
%Y A329877 See A329875 for the corresponding concatenations.
%Y A329877 Cf. A329876.
%K A329877 nonn,base
%O A329877 1,4
%A A329877 _Rémy Sigrist_, Nov 23 2019