A076243 -id:A076243

Search: a076243 -id:a076243

Displaying 1-3 of 3 results found.

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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

A076241

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

+10
3

0, 1, 2, 1, 1, 5, 3, 3, 2, 9, 6, 1, 10, 9, 1, 1, 5, 13, 8, 13, 10, 5, 17, 5, 9, 1, 23, 27, 19, 17, 27, 3, 14, 15, 19, 13, 31, 17, 16, 31, 38, 37, 35, 27, 31, 21, 28, 17, 12, 47, 43, 43, 39, 31, 26, 45, 13, 1, 17, 23, 17, 53, 11, 15, 1, 53, 10, 25, 64, 41, 38, 41, 68, 33, 59, 63, 65

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

OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = A006450(n) mod n.

MATHEMATICA

Table[Mod[Prime[Prime[n]], n], {n, 100}] (* Vincenzo Librandi, Jul 10 2017 *)

PROG

(PARI) a(n) = prime(prime(n)) % n; \\ Michel Marcus, Jul 09 2017

(Magma) [NthPrime(NthPrime(n)) mod(n): n in [1..100]]; // Vincenzo Librandi, Jul 10 2017

CROSSREFS

Cf. A006450, A038580, A049090, A049203, A049202, A057809, A076240-A076243.

KEYWORD

nonn

AUTHOR

Labos Elemer, Oct 08 2002

STATUS

approved

A076242

Remainder when 3rd order prime A038580(n) is divided by n-th prime=A000040(n).

+10
3

1, 2, 1, 3, 6, 10, 5, 8, 17, 19, 27, 31, 38, 35, 28, 39, 17, 17, 10, 38, 68, 63, 13, 55, 48, 4, 74, 100, 37, 29, 47, 121, 115, 136, 105, 28, 128, 109, 159, 90, 114, 31, 151, 4, 86, 108, 81, 147, 149, 189, 185, 119, 231, 166, 88, 238, 197, 233, 64, 186, 258, 111, 128, 260

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

OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Mod[A038580(n), A000040(n)]

MATHEMATICA

Table[Mod[Prime[Prime[Prime[n]]], Prime[n]], {n, 70}] (* Harvey P. Dale, Sep 28 2013 *)

CROSSREFS

Cf. A006450, A038580, A049090, A049203, A049202, A057809, A076240-A076243.

KEYWORD

nonn,less

AUTHOR

Labos Elemer, Oct 08 2002

STATUS

approved

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