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A094998 a(n) is smallest positive integer multiple of n-th prime, say k*prime(n), such that k*prime(n) == 1 (mod j) for each integer j with 1 < j < prime(n). 6
2, 3, 25, 301, 25201, 83161, 7207201, 49008961, 698377681, 2248776129601, 39594522567601, 2599263952084801, 160287943711896001, 4381203794791824001, 386203114510899285601, 130159869178331861668801 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Dimitri Papadopoulos, Table of n, a(n) for n = 1..167

FORMULA

a(n) = A099795(n) * A099796(n) + 1 = A099794(n) * prime(n).

log(a(n)) = prime(n) (approximately, empirical observation). - Dimitri Papadopoulos, Dec 27 2018

EXAMPLE

For n = 1 there are no such j, so the condition is vacuously satisfied and we can take k=1, getting a(1)=2. - N. J. A. Sloane, Feb 10 2015

MATHEMATICA

a[1] = 2; a[2] = 3; a[n_] := Module[{p, m, r, r0, r1}, p = Prime[n]; m = LCM @@ Range[2, p - 1]; r = Reduce[k > 0 && p*k + m*j == 1, {k, j}, Integers]; r0 = r /. C[_] -> 0; r1 = r /. C[_] -> 1; If[r0 === False, r1[[1, 2]], Min[r0[[1, 2]], r1[[1, 2]]]]*p]; Table[a[n], {n, 1, 20}] (* Jean-Fran├žois Alcover, Feb 09 2015 *)

PROG

(MAGMA) /* By definition (slow): */

S:=[]; for n in [1..9] do k:=1; while not forall{j: j in [2..NthPrime(n)-1] | IsOne(k*NthPrime(n) mod j)} do k:=k+1; end while; Append(~S, k*NthPrime(n)); end for; S; /* or */

[p eq 2 select p else Modinv(p, Lcm([1..p-1]))*p: p in PrimesUpTo(60)]; // Bruno Berselli, Feb 08 2015

(PARI) a(n) = {p=prime(n); k=1; for(n=2, p-1, k=lcm(k, n)); for(j=1, p, if((j*k+1)/p==ceil((j*k+1)/p), t=j*k+1; break())); return(t); } \\ Dimitri Papadopoulos, Dec 28 2018

CROSSREFS

Cf. A099794, A099795, A099796.

Sequence in context: A281169 A296281 A226018 * A208203 A109586 A060371

Adjacent sequences:  A094995 A094996 A094997 * A094999 A095000 A095001

KEYWORD

nonn

AUTHOR

Mark Troll (mtroll(AT)u.washington.edu), Oct 22 2004

EXTENSIONS

Edited and extended by Ray Chandler, Oct 29 2004

Added "positive" to definition. - N. J. A. Sloane, Feb 10 2015

STATUS

approved

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Last modified February 25 11:14 EST 2020. Contains 332234 sequences. (Running on oeis4.)