A136251 a(n) = n-th prime reduced modulo the sum of its digits.

0, 0, 0, 0, 1, 1, 1, 9, 3, 7, 3, 7, 1, 1, 3, 5, 3, 5, 2, 7, 3, 15, 6, 4, 1, 1, 3, 3, 9, 3, 7, 1, 5, 9, 9, 4, 1, 3, 13, 8, 9, 1, 4, 11, 10, 9, 3, 6, 7, 8, 1, 1, 3, 3, 5, 10, 14, 1, 5, 6, 10, 13, 7, 1, 5, 9, 2, 12, 11, 13, 1, 2, 15, 9, 18, 5, 9, 17, 1, 6, 13, 1, 7, 3, 7, 3, 7, 9, 10, 8, 8, 19, 12, 1, 15, 7, 5

Offset: 1

Author

Odimar Fabeny, Mar 17 2008

Keywords

• easy
• nonn
• base

Comments

First occurrence of k: A138792. - Robert G. Wilson v, Mar 27 2008

Examples

			2 = 2*1 + 0
3 = 3*1 + 0
5 = 5*1 + 0
7 = 7*1 + 0
11 = 2*5 + 1 (the sum of the digits of 11 is equal to 2)
13 = 4*3 + 1
17 = 8*2 + 1
19 = 10*1 + 9
		

Links

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

Crossrefs

Cf. A000040, A070635, A138791, A138792, A347702.

Programs

Maple

P := select(isprime, [2,seq(i,i=3..10^3,2)]):
map(p -> p mod convert(convert(p,base,10),`+`), P); # Robert Israel, Mar 05 2024

Mathematica

f[n_] := Block[{p = Prime@n}, Mod[p, Plus @@ IntegerDigits@p]]; Array[f, 97] (* Robert G. Wilson v, Mar 27 2008 *)

PARI

a(n) = my(p=prime(n)); p % sumdigits(p); \\ Michel Marcus, Mar 07 2023

Formula

a(n) = A070635(A000040(n)). - Michel Marcus, Mar 07 2023

Extensions

More terms from Robert G. Wilson v, Mar 27 2008