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A247592 Numbers n such that A002496(n) mod A002496(n-1) is a perfect square. 1
2, 8, 10, 25, 42, 147, 160, 169, 238, 260, 491, 544, 869, 890, 923, 1140, 1337, 1386, 1465, 1643, 1927, 3371, 4614, 5038, 5086, 5225, 5832, 5909, 5995, 7118, 7157, 8540, 9859, 12543, 13505, 13795, 13841, 14211, 15347, 17079, 17263, 18643, 20211, 21184, 21245 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A002496 : primes of form n^2+1.

The prime numbers of the sequence are 2, 491, 3371, 9859, 13841,...

The corresponding squares A002496(n) mod A002496 (n-1) are : {1, 144, 100, 1024, 4900, 10816, 11664, 12544,...} = {1} union {A216330} minus {64}.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..200

EXAMPLE

a(3)=10 because A002496(10) mod A002496(9)= 677 mod 577 = 10^2.

MAPLE

with(numtheory):nn:=360000:T:=array(1..nn):kk:=0:

for n from 1 to nn do:

  if type(n^2+1, prime)=true then

   kk:=kk+1:T[kk]:=n^2+1:

   else

   fi:

od:

    for m from 1 to kk-1 do:

     r:=irem(T[m+1], T[m]):z:=sqrt(r):

      if z=floor(z)

       then printf(`%d, `, m+1):

       else

      fi:

    od:

MATHEMATICA

lst={}; lst1={}; nn=400000; Do[If[PrimeQ[n^2+1], AppendTo[lst, n^2+1]], {n, 1, nn}]; nn1:=Length[lst];

Do[If[IntegerQ[Sqrt[Mod[lst[[m]], lst[[m-1]]]]], AppendTo[lst1, m]], {m, 2, nn1}]; lst1

PROG

(Python)

from gmpy2 import t_mod, is_square, is_prime

A247592_list, A002496_list, m, c = [], [2], 2, 2

for n in range(1, 10**7):

....m += 2*n+1

....if is_prime(m):

........if is_square(t_mod(m, A002496_list[-1])):

............A247592_list.append(c)

........A002496_list.append(m)

........c += 1 # Chai Wah Wu, Sep 20 2014

CROSSREFS

Cf. A002496, A193558, A216330.

Sequence in context: A106358 A209449 A002510 * A102943 A062880 A066707

Adjacent sequences:  A247589 A247590 A247591 * A247593 A247594 A247595

KEYWORD

nonn

AUTHOR

Michel Lagneau, Sep 20 2014

STATUS

approved

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Last modified October 22 04:04 EDT 2018. Contains 316431 sequences. (Running on oeis4.)