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A302660 a(n) = (prime(n) mod 9) + (prime(n) mod 10). 1
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", "))}

(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

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)