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 A133905 Least composite number m such that binomial(n+m,m) mod m = 1. 2
 4, 9, 25, 10, 26, 9, 9, 9, 6, 4, 4, 34, 34, 85, 289, 4, 4, 57, 87, 8, 8, 25, 25, 25, 134, 4, 4, 15, 15, 111, 111, 4, 4, 8, 8, 10, 10, 121, 121, 82, 86, 4, 4, 49, 49, 49, 49, 4, 4, 265, 68, 10, 10, 8, 8, 6, 9, 4, 4, 194, 194, 469, 249, 4, 4, 44, 44, 146, 146, 16, 16, 6, 6, 4, 4, 162 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE a(1)=4, since binomial(1+4,4) mod 4 = 5 mod 4 = 1 and 4 is the minimal composite number with this property. a(5)=26 because of binomial(5+26,26)=169911=6535*26+1, but binomial(5+k,k) mod k<>1 for all composite numbers <26. MATHEMATICA lcn[n_]:=Module[{m=4}, While[PrimeQ[m]||Mod[Binomial[n+m, m], m]!=1, m++]; m]; Array[lcn, 80] (* Harvey P. Dale, May 13 2022 *) PROG (PARI) a(n) = { my(m = 4, ok = 0); until (ok, if (! isprime(m) && (binomial(n+m, m) % m == 1), ok = 1, m++); ); return (m); } \\ Michel Marcus, Jul 15 2013 CROSSREFS Cf. A000040, A133620, A133621, A133623, A133630, A133635. Cf. A133872, A133880, A133890, A133900, A133910. Sequence in context: A353978 A334656 A175121 * A131826 A366786 A051961 Adjacent sequences: A133902 A133903 A133904 * A133906 A133907 A133908 KEYWORD nonn AUTHOR Hieronymus Fischer, Oct 20 2007 STATUS approved

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Last modified February 29 20:48 EST 2024. Contains 370428 sequences. (Running on oeis4.)