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A163464
Cumulative sum of a repeated shift-and-add operation on the base-7 representation of prime(n).
1
0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 16, 16, 17, 17, 18, 20, 20, 21, 21, 24, 24, 25, 26, 26, 27, 28, 28, 30, 30, 32, 32, 34, 35, 36, 36, 37, 38, 38, 40, 41, 42, 43, 43, 44, 45, 45, 46, 49, 50, 50, 51, 53, 54, 57, 57, 58, 59, 60, 61, 62
OFFSET
1,7
COMMENTS
Starting from the base-7 representation of prime(n) = d_m*7^m + ... + d_3*7^3 + d_2*7^2 + d_1*7 + d_0, the least-significant digit is recursively removed (a shift-right operation in base 7), and the intermediate numbers are all added up:
a(n) = (d_m*7^(m-1) + ... + d_3*7^2 + d_2*7 + d_1)
+ (d_m*7^(m-2) + ... + d_4*7^2 + d_3*7 + d_2)
+ (d_m*7^(m-3) + ... + d_4*7 + d_3)
+ ... + d_m
= Sum_{j=1..m} d_j*(7^j - 1)/6.
LINKS
MAPLE
shiftadd := proc(n, b) dgs := convert(n, base, b) ; add( op(i, dgs)*(b^(i-1)-1), i=2..nops(dgs))/(b-1) ; end:
A163464 := proc(n) shiftadd(ithprime(n), 7) ; end:
seq(A163464(n), n=1..40) ; # R. J. Mathar, Aug 02 2009
MATHEMATICA
lst={}; Do[p=Prime[n]; s=0; While[p>1, p=IntegerPart[p/7]; s+=p; ]; AppendTo[lst, s], {n, 6!}]; lst
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
EXTENSIONS
Definition rewritten by R. J. Mathar, Aug 02 2009
STATUS
approved