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

1,1

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

Crossrefs

Cf. A007652, A038194.

Sequence in context: A079524 A141740 A088135 * A255005 A137699 A144592

Adjacent sequences: A302657 A302658 A302659 * A302661 A302662 A302663

Keyword

nonn,easy

Author

Dimitris Valianatos, Apr 11 2018

Status

approved