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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A178344 a(n) = Sum_i prime(i+1)^b(i) where n = Sum_{i>=0} b(i)*2^e(i) is the binary representation of n.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 15, 16, 17, 18, 19, 20, 21, 22, 21, 22, 23, 24, 25, 26, 27, 28, 18, 19, 20, 21, 22, 23, 24, 25, 24, 25, 26, 27, 28, 29, 30, 31, 28, 29, 30, 31, 32, 33, 34, 35, 34, 35, 36, 37, 38, 39, 40, 41, 23, 24, 25, 26, 27, 28, 29, 30, 29, 30
Offset: 0

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Author

Juri-Stepan Gerasimov, May 25 2010, Jan 06 2010

Keywords

Comments

a(0) = 0 might be a more logical value for the initial term. - Antti Karttunen, Sep 28 2018

Examples

			a(16)=15 because 10000 is the base-2 representation of n=16 and 11^1 + 7^0 + 5^0 + 3^0 + 2^0 = 15.
		

Crossrefs

Cf. A178562 (first differences).

Programs

  • Maple
    A178344 := proc(n)
        if n = 0 then
            dgs := [0] ;
        else
            dgs := convert(n,base,2) ;
        end if;
        add(ithprime(i)^dgs[i],i=1..nops(dgs)) ;
    end proc:
    seq(A178344(n),n=0..73) ; # R. J. Mathar, Sep 28 2018
  • Mathematica
    Array[Total@ MapIndexed[Prime[First@ #2]^#1 &, Reverse@ IntegerDigits[#, 2]] &, 74, 0] (* Michael De Vlieger, Feb 19 2019 *)
  • PARI
    a(n) = my(b=Vecrev(binary(n))); if (n==0, b=[0]); sum(i=1, #b, prime(i)^b[i]); \\ Michel Marcus, Sep 29 2018

Formula

For n >= 1, a(n) = A089625(n) + A080791(n). - Antti Karttunen, Sep 28 2018

Extensions

Offset modified, keyword:base added by R. J. Mathar, May 28 2010
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