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.

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

Offset: 0

Author

James Burling, Oct 08 2015

Keywords

• nonn
• base
• easy

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 subtables:

Subtable 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

Subtable 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

Subtable 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 subtable is 10 X 10. Let T_n(j,k) = the element in the j-th row of the k-th column of subtable 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)

Examples

			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.
		

Links

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

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).

Programs

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 *)

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

Formula

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