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.

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, 134, 94, 84, 6, 57, 103, 13, 92, 63, 90, 60, 156, 39, 10, 108, 114, 65, 78, 67, 52, 57, 11, 21, 114, 79, 366, 128, 76, 22, 382, 36, 88, 34, 68, 110, 2, 72, 14, 28

Offset

1,4

Comments

This sequence is a binary variant of A329876.

For any n > 0, the binary concatenation of a(n+1) and A329875(n) gives A329875(n+1).

Links

Table of n, a(n) for n=1..66.

Example

The first terms, alongside their binary representations and the corresponding concatenations, are:
  n   a(n)  bin(a(n))  bin(A329875(n))
  --  ----  ---------  -----------------------
   1     1          1                        1
   2     1          1                       11
   3     1          1                      111
   4     2         10                    10111
   5     4        100                 10010111
   6     3         11               1110010111
   7     7        111            1111110010111
   8    10       1010        10101111110010111
   9    18      10010   1001010101111110010111
  10     1          1  11001010101111110010111

Prog

(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)))

Crossrefs

See A329875 for the corresponding concatenations.

Cf. A329876.

Sequence in context: A207633 A177877 A090568 * A223625 A166017 A257504

Adjacent sequences: A329874 A329875 A329876 * A329878 A329879 A329880

Keyword

nonn,base

Author

Rémy Sigrist, Nov 23 2019

Status

approved