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

Offset: 1

Author

Dimitris Valianatos, Apr 11 2018

Keywords

• nonn
• easy

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}.

Examples

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

Links

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

Crossrefs

Cf. A007652, A038194.

Programs

Magma

[(NthPrime(n) mod 9) + (NthPrime(n) mod 10): n in [1..100]]; // Vincenzo Librandi, Jun 10 2018

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 *)

PARI

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

Formula

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