A163464 Cumulative sum of a repeated shift-and-add operation on the base-7 representation of prime(n).

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

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

Cf. A080085, A080086, A080087.

Sequence in context: A366701 A278496 A353283 * A317137 A139327 A076905

Adjacent sequences: A163461 A163462 A163463 * A163465 A163466 A163467

Keyword

nonn,easy,base

Author

Vladimir Joseph Stephan Orlovsky, Jul 28 2009

Extensions

Definition rewritten by R. J. Mathar, Aug 02 2009

Status

approved