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A180507 Numbers k such that k^2 + 1 = p*q, p and q prime with p == q (mod k). 0
3, 8, 12, 144, 1020, 8040, 13860, 34840, 729180, 1728240, 17576520, 85184880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

q - p = k with k = 3, 8, 144.

The next terms with q - p = k are F(432) = 85738...5984 and F(570) where F(n) is the n-th Fibonacci number. All such terms are in A001906; the next such term, if one exists, has more than 25,000 decimal digits. [From Charles R Greathouse IV, Jan 21 2011]

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

a(3) = 12 because 12^2 + 1 = 5*29 and 29 - 5 = 2*12 ;

a(8) = 34840 because 34840^2 + 1 = 4289 * 283009 and 283009 - 4289 = 278720 = 8*34840

MAPLE

with(numtheory):for k from 1 to 40000 do: x:=k^2+1:y:=factorset(x):yy:=bigomega(x):if

  yy=2 and irem(y[2], k) =y[1] then printf(`%d, `, k):else fi:od:

CROSSREFS

Subset of A085722.

Cf. A134406, A134407, A027862, A002496, A005574.

Sequence in context: A032142 A032046 A247396 * A218889 A131213 A320260

Adjacent sequences:  A180504 A180505 A180506 * A180508 A180509 A180510

KEYWORD

nonn,hard

AUTHOR

Michel Lagneau, Jan 20 2011

EXTENSIONS

a(9)-a(12) from Charles R Greathouse IV, Jan 24 2011.

STATUS

approved

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Last modified May 19 08:25 EDT 2019. Contains 323389 sequences. (Running on oeis4.)