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A263042 a(n) = Sum_{i >= 1} d_i(n) * prime(i) where d_i(n) is the i-th digit of n in base 10, and prime(i) is the i-th prime. 1
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Digits are counted from the right, so d_1(n) is the ones digit, d_2(n) is the tens digit, etc.

d_i(n) can be found using either of the following formulas:

* d_i(n) = floor(n) / 10^(i-1)) mod 10;

* d_i(n) = floor(n / 10^(i-1)) - 10 * floor(n / 10^i).

From Derek Orr, Dec 24 2015: (Start)

For n < 1000, this sequence may be written as a series of 10 X 10 sub-tables:

Sub-table 1:

   0,  2,  4,  6,  8, 10, 12, 14, 16, 18

   3,  5,  7,  9, 11, 13, 15, 17, 19, 21

   6,  8, 10, 12, 14, 16, 18, 20, 22, 24

   9, 11, 13, 15, 17, 19, 21, 23, 25, 27

  12, 14, 16, 18, 20, 22, 24, 26, 28, 30

  15, 17, 19, 21, 23, 25, 27, 29, 31, 33

  18, 20, 22, 24, 26, 28, 30, 32, 34, 36

  21, 23, 25, 27, 29, 31, 33, 35, 37, 39

  24, 26, 28, 30, 32, 34, 36, 38, 40, 42

  27, 29, 31, 33, 35, 37, 39, 41, 43, 45

Sub-table 2:

   5,  7,  9, 11, 13, 15, 17, 19, 21, 23

   8, 10, 12, 14, 16, 18, 20, 22, 24, 26

  11, 13, 15, 17, 19, 21, 23, 25, 27, 29

  14, 16, 18, 20, 22, 24, 26, 28, 30, 32

  17, 19, 21, 23, 25, 27, 29, 31, 33, 35

  20, 22, 24, 26, 28, 30, 32, 34, 36, 38

  23, 25, 27, 29, 31, 33, 35, 37, 39, 41

  26, 28, 30, 32, 34, 36, 38, 40, 42, 44

  29, 31, 33, 35, 37, 39, 41, 43, 45, 47

  32, 34, 36, 38, 40, 42, 44, 46, 48, 50

Sub-table 3:

  10, 12, 14, 16, 18, 20, 22, 24, 26, 28

  13, 15, 17, 19, 21, 23, 25, 27, 29, 31

  16, 18, 20, 22, 24, 26, 28, 30, 32, 34

  19, 21, 23, 25, 27, 29, 31, 33, 35, 37

  22, 24, 26, 28, 30, 32, 34, 36, 38, 40

  25, 27, 29, 31, 33, 35, 37, 39, 41, 43

  28, 30, 32, 34, 36, 38, 40, 42, 44, 46

  31, 33, 35, 37, 39, 41, 43, 45, 47, 49

  34, 36, 38, 40, 42, 44, 46, 48, 50, 52

  37, 39, 41, 43, 45, 47, 49, 51, 53, 55

  ...

Each sub-table is 10 X 10. Let T_n(j,k) = the element in the j-th row of the k-th column of sub-table n. T_n(1,1) = 5*(n-1). T_n(j,1) = 5*(n-1)+3*(j-1). T_n(1,k) = 5*(n-1)+2*(k-1). Altogether, T_n(j,k) = 5*(n-1)+3*(j-1)+2*(k-1) = 5*n+3*j+2*k-10.

(End)

LINKS

James Burling, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{i >= 0} prime(i + 1) * (floor(n / 10^i) - 10 * floor(n / 10^(i + 1))).

EXAMPLE

For n = 12, the digits are 2 and 1 and the corresponding primes are 2 and 3, so a(12) = (first digit * first prime) + (second digit * second prime) = 2 * 2 + 1 * 3 = 4 + 3 = 7.

MATHEMATICA

Table[Sum_{m=0}^{infinity} (Floor[n/10^(m)] - 10*Floor[n/10^(m+1)])*Prime(m+1), {n, 0, 500}] (* G. C. Greubel, Oct 08 2015 *)

PROG

(PARI) a(n) = if (n==0, d = [0], d=Vecrev(digits(n))); sum(i=1, #d, d[i]*prime(i)); \\ Michel Marcus, Oct 10 2015

(PARI) vector(200, n, n--; sum(i=1, #digits(n), Vecrev(digits(n))[i]*prime(i))) \\ Derek Orr, Dec 24 2015

CROSSREFS

Similar method, different base for n: A089625 (base 2), A262478 (base 3).

Similar method, uses product instead of sum: A019565 (base 2), A101278 (base 3), A054842 (base 10).

Sequence in context: A245627 A097586 A169805 * A230099 A098727 A182324

Adjacent sequences:  A263039 A263040 A263041 * A263043 A263044 A263045

KEYWORD

nonn,base,easy

AUTHOR

James Burling, Oct 08 2015

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)