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

1, 1101, 11011101, 1101110011101, 1101110010110011101, 1101110010111010110011101, 1101110010111011111010110011101, 11011100101110111100011111010110011101, 1101110010111011110001001100011111010110011101, 110111001011101111000100110101001100011111010110011101

Offset: 1

Author

N. J. A. Sloane, Feb 18 2023

Keywords

• nonn
• base

Comments

Binary analog of A173426 and A360504.

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

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.

Links

• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Cf. A007088, A173426, A173427, A360504.

Programs

Maple

a:= n-> parse(cat(map(t-> convert(t, binary), [$1..n, n-i$i=1..n-1])[])):
seq(a(n), n=1..10);  # Alois P. Heinz, Feb 18 2023

Mathematica

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

Python

from itertools import count, islice
def agen(): # generator of terms
    sl, sr, sk = "", "", "1"
    for k in count(1):
        sk = bin(k)[2:]
        sl += sk
        yield int(sl + sr)
        sr = sk + sr
print(list(islice(agen(), 10))) # Michael S. Branicky, Feb 18 2023