A076241 -id:A076241

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A076240

Remainder when 2nd order prime pp(n) = A006450(n) is divided by n-th prime = A000040(n).

+10
6

1, 2, 1, 3, 9, 2, 8, 10, 14, 22, 3, 9, 15, 19, 23, 29, 41, 39, 63, 69, 2, 6, 16, 16, 24, 42, 48, 52, 54, 52, 74, 84, 88, 102, 114, 122, 134, 152, 156, 166, 168, 1, 7, 13, 19, 23, 31, 71, 71, 73, 73, 65, 77, 91, 79, 91, 109, 115, 125, 137, 149, 155, 185, 197, 203, 197, 235

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = prime^2(n) mod prime(n) = A006450(n) mod A000040(n).

EXAMPLE

a(4) = 3 since prime(prime(4)) (mod prime(4)) = prime(7) (mod 7) = 17 (mod 7) = 3. - Michael De Vlieger, Mar 25 2017

MAPLE

a:= n-> (p-> irem(ithprime(p), p))(ithprime(n)):

seq(a(n), n=1..70); # Alois P. Heinz, Oct 09 2015

MATHEMATICA

Table[Mod @@ Map[Nest[Prime, n, #] &, {2, 1}], {n, 65}] (* Michael De Vlieger, Mar 25 2017 *)

PROG

(PARI) a(n) = prime(prime(n)) % prime(n); \\ Michel Marcus, Mar 25 2017

CROSSREFS

Cf. A006450, A038580, A049090, A049203, A049202, A057809, A076241, A076242, A076243.

KEYWORD

nonn,look

AUTHOR

Labos Elemer, Oct 08 2002

STATUS

approved

A076243

Remainder when 3rd-order prime ppp(n) = A038580(n) is divided by n.

+10
4

0, 1, 1, 3, 2, 5, 4, 3, 8, 9, 5, 7, 10, 5, 7, 3, 2, 11, 17, 1, 20, 21, 11, 19, 12, 17, 14, 17, 18, 19, 18, 23, 28, 27, 11, 19, 15, 7, 2, 21, 40, 25, 31, 1, 19, 15, 9, 31, 46, 47, 10, 15, 43, 23, 14, 9, 17, 19, 18, 41, 24, 27, 50, 3, 14, 29, 13, 3, 4, 39, 21, 1, 47, 19, 31, 13, 6, 17

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = ppp(n) mod n = A038580(n) mod n.

MATHEMATICA

MapIndexed[Mod[#1, First@ #2] &, Nest[Prime, Range@ 79, 3]] (* Michael De Vlieger, Jul 22 2017 *)