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 A134406 Composite numbers of the form k^2 + 1. 18
 10, 26, 50, 65, 82, 122, 145, 170, 226, 290, 325, 362, 442, 485, 530, 626, 730, 785, 842, 901, 962, 1025, 1090, 1157, 1226, 1370, 1445, 1522, 1682, 1765, 1850, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602, 2705, 2810, 3026, 3250, 3365, 3482, 3601, 3722, 3845 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Square roots of these numbers are quadratic irrationals and corresponding chain fraction representations are periodic: sqrt(10) = [3;{2,3}], sqrt(26) = [5;{2,5}], sqrt(50) = [7;{2,7}], ..., where {} is denoted a period (we write {6} == {2,3}). LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = 1 + A134407(n)^2. - R. J. Mathar, Oct 13 2019 EXAMPLE 10 is a term because 10 = 3^2 + 1 is composite, 26 is a term because 26 = 5^2 + 1 is composite, 50 is a term because 50 = 7^2 + 1 is composite. MAPLE ts_fn1:=proc(n) local i, tren, ans; ans:=[ ]: for i from 1 to n do tren := i^(2)+1: if (isprime(tren) = false) then ans:=[ op(ans), tren ]: fi od: RETURN(ans) end: ts_fn1(200); MATHEMATICA Select[Range^2+1, !PrimeQ[#]&] (* Harvey P. Dale, Aug 12 2012 *) PROG (PARI) for(n=3, 99, if(!isprime(t=n^2+1), print1(t", "))) \\ Charles R Greathouse IV, Aug 29 2016 (Python) from sympy import isprime from itertools import count, takewhile def aupto(limit):     form = takewhile(lambda x: x <= limit, (k**2+1 for k in count(1)))     return [number for number in form if not isprime(number)] print(aupto(3845)) # Michael S. Branicky, Oct 26 2021 CROSSREFS Cf. A002496, A005574, A134407. Supersequence of A144255. Sequence in context: A299409 A198017 A137351 * A099978 A242719 A242489 Adjacent sequences:  A134403 A134404 A134405 * A134407 A134408 A134409 KEYWORD nonn AUTHOR Jani Melik, Jan 18 2008 STATUS approved

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Last modified October 6 08:17 EDT 2022. Contains 357263 sequences. (Running on oeis4.)