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 A327652 Intersection of A099011 and A327651. 5
 169, 385, 961, 1121, 3827, 6265, 6441, 6601, 7801, 8119, 10945, 13067, 15841, 18241, 19097, 20833, 24727, 27971, 29953, 31417, 34561, 35459, 37345, 38081, 39059, 42127, 45961, 47321, 49105, 52633, 53041, 55969, 56953, 58241, 62481, 74305, 79361, 81361, 84587, 86033, 86241, 101311, 107801 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let {x(n)} be a sequence defined by x(0) = 0, x(1) = 1, x(n) = m*x(n-1) + x(n-2) for k >= 2. For primes p, we have (a) p divides x(p-((m^2+4)/p); (b) x(p) == ((m^2+4)/p) (mod p), where (D/p) is the Kronecker symbol. This sequence gives composite numbers k such that gcd(k, m^2+4) = 1 and that conditions similar to (a) and (b) hold for k simultaneously, where m = 2. If k is not required to be coprime to m^2 + 4 (= 8), then there are 1190 such k <= 10^5 and 4847 such k <= 10^6, while there are only 41 terms <= 10^5 and 119 terms <= 10^6 in this sequence. LINKS Daniel Suteu, Table of n, a(n) for n = 1..10000 EXAMPLE 169 divides Pell(168) as well as Pell(169) - 1, so 169 is a term. PROG (PARI) pellmod(n, m)=((Mod([2, 1; 1, 0], m))^n)[1, 2] isA327652(n)=!isprime(n) && pellmod(n, n)==kronecker(8, n) && !pellmod(n-kronecker(8, n), n) && gcd(n, 8)==1 && n>1 CROSSREFS m m=1 m=2 m=3 k | x(k-Kronecker(m^2+4,k))* A081264 U A141137 A327651 A327653 k | x(k)-Kronecker(m^2+4,k) A049062 A099011 A327654 both A212424 this seq A327655 * k is composite and coprime to m^2 + 4. Cf. A000129, A091337 ({Kronecker(8,n)}). Sequence in context: A099011 A330276 A351337 * A112076 A305055 A069645 Adjacent sequences: A327649 A327650 A327651 * A327653 A327654 A327655 KEYWORD nonn AUTHOR Jianing Song, Sep 20 2019 STATUS approved

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Last modified June 10 03:49 EDT 2023. Contains 363187 sequences. (Running on oeis4.)