A302660 - OEIS

A302660

a(n) = (prime(n) mod 9) + (prime(n) mod 10).

4, 6, 10, 14, 3, 7, 15, 10, 8, 11, 5, 8, 6, 10, 9, 11, 14, 8, 11, 9, 4, 16, 5, 17, 14, 3, 7, 15, 10, 8, 8, 6, 9, 13, 14, 8, 11, 4, 12, 5, 17, 2, 3, 7, 15, 10, 5, 10, 9, 13, 11, 14, 8, 9, 12, 5, 17, 2, 14, 3, 7, 8, 8, 6, 10, 9, 8, 11, 12, 16, 5, 17, 14, 7, 10, 8, 11, 8, 6, 13, 14, 8, 9, 4, 16, 5, 17, 14, 3, 7, 15, 11, 8, 6, 13

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The sum (prime(n) mod 9 + prime(n) mod 10) gives numbers between 2 and 17.

For large n the distribution is displayed in the diagram below.

3y| .. . . . . . . . . .. o o

| /:\ /:\

| / : \ / : \

2y| .. . . . . . o / : o--o : \ o

| /:\ / : : : : \ /:\

| / | \ / : | | : \ / | \

y| .. o--o--o : o--o : : : : o--o : o--o--o

| /. . . | . . : | | : . . | . . .\

| / . . . : . . : : : : . . : . . . \

|__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__\

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 /

If y is the quantity for {2, 3, 4, 6, 7, 12, 13, 15, 16, 17} (same)

then 2y is the quantity of {5, 9, 10, 14} (same) and

3y is the quantity for {8, 11} (same).

Example: For primes less than 10^10, the distribution of frequencies of a(n) from 2 to 17 is {18960677, 18960726, 18960712, 37920181, 18959991, 18960427, 56880630, 37923467, 37921201, 56882003, 18960991, 18960869, 37920879, 18960270, 18959802, 18959685}.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A038194(n) + A007652(n).

EXAMPLE

For n=7, prime(7) = 17, 17 mod 9 = 8 and 17 mod 10 = 7. So a(7) = 8 + 7 = 15.

MAPLE

map(t -> (t mod 9)+(t mod 10), [seq(ithprime(i), i=1..100)]); # Robert Israel, Jun 10 2018

MATHEMATICA

Array[Mod[#, 9] + Mod[#, 10] &@ Prime@ # &, 95] (* Michael De Vlieger, Apr 21 2018 *)

PROG

(PARI) {forprime(n = 2, 1000, s = n%9 + n%10; print1(s", "))}