cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A362411 Numbers k such that A359149(k) is prime when interpreted as a binary number.

Original entry on oeis.org

2, 4, 38, 2861
Offset: 1

Views

Author

Michael S. Branicky, Apr 18 2023

Keywords

Examples

			A359149(2) = 1101_2 = 13_10 is prime, so 2 is a term.
A359149(4) = 1101110011101_2 = 7069_10 is prime, so 4 is a term.
		

Crossrefs

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.

Original entry on oeis.org

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

Views

Author

Umut Uludag, Feb 18 2010

Keywords

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

Examples

			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.
		

Crossrefs

Cf. A359149 (binary representations).

Programs

  • 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
  • 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<>b&&b++;s=s<>b&&b++;(s<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

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))
Showing 1-2 of 2 results.