A173427 Decimal value a(n) of the binary number b(n) obtained by starting from 1, sequentially concatenating all binary numbers up to n and then sequentially concatenating all binary numbers from n-1 down to 1.

1, 13, 221, 7069, 451997, 28931485, 1851651485, 237010810269, 60674754606493, 15532737233548701, 3976380732916495773, 1017953467644930815389, 260596087717395474544029, 66712598455657932715586973, 17078425204648505835166758301, 8744153704780027821877938484637

Offset

1,2

Comments

a(2) = 13 and a(4) = 7069 are primes. What other terms are primes? - N. J. A. Sloane, Feb 18 2023

a(38) is the next prime. - Michael S. Branicky, Feb 18 2023

Links

Amiram Eldar, Table of n, a(n) for n = 1..239

Index entries for sequences related to Most Wanted Primes video

Formula

a(n) = binary_to_decimal(concatenate(1,10,11,..., binary(n-2), binary(n-1), binary(n), binary(n-1), binary(n-2),..., 11, 10, 1))

Example

a(1)=binary_to_decimal(1)=1, a(2)=binary_to_decimal(1101)=13, a(3)=binary_to_decimal(11011101)=221, a(4)=binary_to_decimal(1101110011101)=7069 etc.

Maple

a:= n-> Bits[Join](map(x-> Bits[Split](x)[], [$1..n, n-i$i=1..n-1])):
seq(a(n), n=1..16);  # Alois P. Heinz, Feb 18 2023

Prog

(PARI) a(n)=sum(i=1, #n=concat(vector(n*2-1, k, binary(min(k, n*2-k)))), n[i]<<(#n-i))
(PARI) A173427(n)={my(s=0, s1=0, t=0, b=0); for(k=1, n-1, s1+=k<<t+=b; k>>b&&b++; s=s<<b+k); t+=b; n>>b&&b++; (s<<b+n)<<t+s1} \\ M. F. Hasler, Aug 06 2015
(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, 2)
        sr = sk + sr
print(list(islice(agen(), 16))) # Michael S. Branicky, Feb 18 2023

Crossrefs

Cf. A359149 (binary representations).

Sequence in context: A329073 A015253 A051621 * A051180 A143832 A140841

Adjacent sequences: A173424 A173425 A173426 * A173428 A173429 A173430

Keyword

base,nonn

Author

Umut Uludag, Feb 18 2010.

Status

approved