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.

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

Author

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

Keywords

• nonn
• base

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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537

Crossrefs

Cf. A000040, A001477, A056791, A007088, A080791, A089625, A143710, A175524.

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