cp's OEIS Frontend

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.

%I A173427 #23 Jul 09 2025 04:32:29
%S A173427 1,13,221,7069,451997,28931485,1851651485,237010810269,60674754606493,
%T A173427 15532737233548701,3976380732916495773,1017953467644930815389,
%U A173427 260596087717395474544029,66712598455657932715586973,17078425204648505835166758301,8744153704780027821877938484637
%N 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.
%C A173427 a(2) = 13 and a(4) = 7069 are primes. What other terms are primes? - _N. J. A. Sloane_, Feb 18 2023
%C A173427 a(38) is the next prime. - _Michael S. Branicky_, Feb 18 2023
%H A173427 Amiram Eldar, <a href="/A173427/b173427.txt">Table of n, a(n) for n = 1..239</a>
%H A173427 <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>
%F A173427 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))
%e A173427 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.
%p A173427 a:= n-> Bits[Join](map(x-> Bits[Split](x)[], [$1..n, n-i$i=1..n-1])):
%p A173427 seq(a(n), n=1..16);  # _Alois P. Heinz_, Feb 18 2023
%o A173427 (PARI) a(n)=sum(i=1,#n=concat(vector(n*2-1,k,binary(min(k, n*2-k)))),n[i]<<(#n-i))
%o A173427 (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
%o A173427 (Python)
%o A173427 from itertools import count, islice
%o A173427 def agen(): # generator of terms
%o A173427     sl, sr, sk = "", "", "1"
%o A173427     for k in count(1):
%o A173427         sk = bin(k)[2:]
%o A173427         sl += sk
%o A173427         yield int(sl + sr, 2)
%o A173427         sr = sk + sr
%o A173427 print(list(islice(agen(), 16))) # _Michael S. Branicky_, Feb 18 2023
%Y A173427 Cf. A359149 (binary representations).
%K A173427 base,nonn
%O A173427 1,2
%A A173427 _Umut Uludag_, Feb 18 2010