The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A255859 Least m > 0 such that gcd(m^n+9,(m+1)^n+9) > 1, or 0 if there is no such m. 4
 1, 0, 18, 533, 1, 32, 288, 484, 1, 364, 6, 176427, 1, 31239, 533, 8, 1, 8424432925592889329288197322308900672459420460792433, 30, 16561, 1, 4, 6, 349, 1, 32, 546, 2579, 1, 375766, 11, 5061867704425915, 1, 5620, 6, 8, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See A118119, which is the main entry for this class of sequences. LINKS Will Wei, Patterns that appear to hold, but don't - 8424432925592889329288197322308900672459420460792433, video (2020) FORMULA a(4k)=1 for k>=0, because gcd(1^(4k)+9, 2^(4k)+9) = gcd(10, 16^k-1) = 5. EXAMPLE For n=1, gcd(m^n+9, (m+1)^n+9) = gcd(m+9, m+10) = 1, therefore a(1)=0. For n=2, we have gcd(18^2+9, 19^2+9) = gcd(333, 370) = 37, and the pair (m,m+1)=(18,19) is the smallest which yields a GCD > 1, therefore a(2)=37. For n=4k, see formula. MATHEMATICA A255859[n_] := Module[{m = 1}, While[GCD[m^n + 9, (m + 1)^n + 9] <= 1, m++]; m]; Join[{1, 0}, Table[A255859[n], {n, 2, 16}]] (* Robert Price, Oct 16 2018 *) PROG (PARI) a(n, c=9, L=10^7, S=1)={n!=1&&for(a=S, L, gcd(a^n+c, (a+1)^n+c)>1&&return(a))} CROSSREFS Cf. A118119, A255832, A255852-A255869 Sequence in context: A126276 A035277 A011906 * A334179 A183498 A254381 Adjacent sequences:  A255856 A255857 A255858 * A255860 A255861 A255862 KEYWORD nonn,hard,more AUTHOR M. F. Hasler, Mar 08 2015 EXTENSIONS a(17)-a(30) from Hiroaki Yamanouchi, Mar 12 2015 a(31)-a(36) from Max Alekseyev, Aug 06 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)