A143710 -id:A143710

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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.

+10
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

(list; graph; refs; listen; history; text; internal format)

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).

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

A144174

(1=1, 2=2, 3=3, 4=2^2, 5=5, 6=2*3, 7=7, 8=2^3, 9=3^2, 10=2*5, 11=11, 12=2^2*3, 13=13, ..) becomes (1+1+2, 2+3+3, 4+2+2, 5+5+6, 2+3+7, 7+8+2, 3+9+3, 2+10+2, 5+11+11, 12+2+2, 3+13+13, ..).

+10
0

4, 8, 8, 16, 12, 17, 15, 14, 27, 16, 29, 23, 23, 22, 52, 7, 58, 9, 31, 35, 70, 8, 32, 41, 33, 32, 65, 35, 67, 39, 47, 53, 47, 40, 42, 77, 61, 55, 49, 85, 53, 89, 58, 10, 71, 142, 9, 58, 57, 56, 71, 68, 109, 61, 72, 12, 79, 89, 178, 7, 127, 95, 68, 73, 76, 81, 81, 137, 88, 96

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

3+13+13=29=a(11).

14+2+7=23=a(12).

15=3+5=23=a(13).

16+2+4=22=a(14).

17+17+18=52=a(15).

2+3+2=7=a(16).

19+19+20=58=a(17),

etc.

CROSSREFS

Cf. A143710, A143711.

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Nov 17 2008

EXTENSIONS

a(1) and all terms from a(13) on corrected by R. J. Mathar, Apr 29 2010

STATUS

approved

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