%I #15 Feb 19 2023 16:17:42

%S 1,1101,11011101,1101110011101,1101110010110011101,

%T 1101110010111010110011101,1101110010111011111010110011101,

%U 11011100101110111100011111010110011101,1101110010111011110001001100011111010110011101,110111001011101111000100110101001100011111010110011101

%N Concatenate the binary strings for 1,2,...,n-1, n, n-1, ..., 2,1.

%C Binary analog of A173426 and A360504.

%C Converting these binary strings to base 10 gives A173427. E.g. 1101_2 = 13_10 gives A173427(3) = 13.

%C What is the first prime here if these strings are regarded as decimal numbers as they stand? a(5) = 1101110010110011101 = 3*37*53*187168113226247 is obviously not a prime.

%H <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>

%p a:= n-> parse(cat(map(t-> convert(t, binary), [$1..n, n-i$i=1..n-1])[])):

%p seq(a(n), n=1..10); # _Alois P. Heinz_, Feb 18 2023

%t a[n_] := FromDigits @ Flatten @ IntegerDigits[Join[Range[1, n], Range[n - 1, 1, -1]], 2]; Array[a, 10] (* _Amiram Eldar_, Feb 18 2023 *)

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o sl, sr, sk = "", "", "1"

%o for k in count(1):

%o sk = bin(k)[2:]

%o sl += sk

%o yield int(sl + sr)

%o sr = sk + sr

%o print(list(islice(agen(), 10))) # _Michael S. Branicky_, Feb 18 2023

%Y Cf. A007088, A173426, A173427, A360504.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Feb 18 2023