A302660 - OEIS

%I #31 Sep 08 2022 08:46:21

%S 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,

%T 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,

%U 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

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

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

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

%C                                                            .

%C     ^

%C     |

%C   3y| .. . . . . . . . . .. o        o

%C     |                      /:\      /:\

%C     |                     / : \    / : \

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

%C     |             /:\    /  :  :  :  :  \    /:\

%C     |            / | \   /  :  |  |  :  \   / | \

%C    y| ..  o--o--o  :  o--o  :  :  :  :  o--o  :  o--o--o

%C     |    /.  .  .  |  .  .  :  |  |  :  .  .  |  .  .  .\

%C     |   / .  .  .  :  .  .  :  :  :  :  .  .  :  .  .  . \

%C     |__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__o__\

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

%C                                                              .

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

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

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

%C 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}.

%H Robert Israel, <a href="/A302660/b302660.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%t Array[Mod[#, 9] + Mod[#, 10] &@ Prime@ # &, 95] (* _Michael De Vlieger_, Apr 21 2018 *)

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

%o (Magma) [(NthPrime(n) mod 9) + (NthPrime(n) mod 10): n in [1..100]]; // _Vincenzo Librandi_, Jun 10 2018

%Y Cf. A007652, A038194.

%K nonn,easy

%O 1,1

%A _Dimitris Valianatos_, Apr 11 2018