|
%I #21 Feb 19 2023 17:03:15
%S 1,13,221,7069,451997,28931485,1851651485,237010810269,60674754606493,
%T 15532737233548701,3976380732916495773,1017953467644930815389,
%U 260596087717395474544029,66712598455657932715586973,17078425204648505835166758301,8744153704780027821877938484637
%N 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 a(2) = 13 and a(4) = 7069 are primes. What other terms are primes? - _N. J. A. Sloane_, Feb 18 2023
%C a(38) is the next prime. - _Michael S. Branicky_, Feb 18 2023
%H Amiram Eldar, <a href="/A173427/b173427.txt">Table of n, a(n) for n = 1..239</a>
%H <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>
%F 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 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 a:= n-> Bits[Join](map(x-> Bits[Split](x)[], [$1..n, n-i$i=1..n-1])):
%p seq(a(n), n=1..16); # _Alois P. Heinz_, Feb 18 2023
%o (PARI) a(n)=sum(i=1,#n=concat(vector(n*2-1,k,binary(min(k, n*2-k)))),n[i]<<(#n-i))
%o (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 (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, 2)
%o sr = sk + sr
%o print(list(islice(agen(), 16))) # _Michael S. Branicky_, Feb 18 2023
%Y Cf. A359149 (binary representations).
%K base,nonn
%O 1,2
%A _Umut Uludag_, Feb 18 2010.
|
