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A359149 Concatenate the binary strings for 1,2,...,n-1, n, n-1, ..., 2,1.

%I A359149 #15 Feb 19 2023 16:17:42
%S A359149 1,1101,11011101,1101110011101,1101110010110011101,
%T A359149 1101110010111010110011101,1101110010111011111010110011101,
%U A359149 11011100101110111100011111010110011101,1101110010111011110001001100011111010110011101,110111001011101111000100110101001100011111010110011101
%N A359149 Concatenate the binary strings for 1,2,...,n-1, n, n-1, ..., 2,1.
%C A359149 Binary analog of A173426 and A360504.
%C A359149 Converting these binary strings to base 10 gives A173427. E.g. 1101_2 = 13_10 gives A173427(3) = 13.
%C A359149 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 A359149 <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>
%p A359149 a:= n-> parse(cat(map(t-> convert(t, binary), [$1..n, n-i$i=1..n-1])[])):
%p A359149 seq(a(n), n=1..10);  # _Alois P. Heinz_, Feb 18 2023
%t A359149 a[n_] := FromDigits @ Flatten @ IntegerDigits[Join[Range[1, n], Range[n - 1, 1, -1]], 2]; Array[a, 10] (* _Amiram Eldar_, Feb 18 2023 *)
%o A359149 (Python)
%o A359149 from itertools import count, islice
%o A359149 def agen(): # generator of terms
%o A359149     sl, sr, sk = "", "", "1"
%o A359149     for k in count(1):
%o A359149         sk = bin(k)[2:]
%o A359149         sl += sk
%o A359149         yield int(sl + sr)
%o A359149         sr = sk + sr
%o A359149 print(list(islice(agen(), 10))) # _Michael S. Branicky_, Feb 18 2023
%Y A359149 Cf. A007088, A173426, A173427, A360504.
%K A359149 nonn,base
%O A359149 1,2
%A A359149 _N. J. A. Sloane_, Feb 18 2023