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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.
3
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
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. A178562 (first differences).
Sequence in context: A081516 A023962 A094562 * A274333 A039241 A000394
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