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

0,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Cf. A178562 (first differences).

Sequence in context: A081516 A023962 A094562 * A274333 A039241 A000394

Adjacent sequences: A178341 A178342 A178343 * A178345 A178346 A178347

Keyword

nonn,base

Author

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

Extensions

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

Status

approved