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Search: id:A163464
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| A163464 |
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Cumulative sum of a repeated shift-and-add operation on the base-7 representation of prime(n). |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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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.
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MAPLE
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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
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MATHEMATICA
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lst={}; Do[p=Prime[n]; s=0; While[p>1, p=IntegerPart[p/7]; s+=p; ]; AppendTo[lst, s], {n, 6!}]; lst
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CROSSREFS
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Cf. A080085, A080086, A080087
Sequence in context: A057358 A038128 A097337 this_sequence A139327 A076905 A098295
Adjacent sequences: A163461 A163462 A163463 this_sequence A163465 A163466 A163467
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KEYWORD
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nonn,easy,base
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 28 2009
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EXTENSIONS
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Definition rewritten by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2009
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