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A085074 Smallest number a(n) == 1 (mod n) such that the prime signature of n and a(n) is the same. 6
3, 7, 9, 11, 55, 29, 4913, 289, 21, 23, 325, 53, 15, 46, 81, 103, 325, 191, 261, 22, 111, 47, 3625, 10201, 183, 6859, 477, 59, 1771, 311, 8587340257, 34, 35, 106, 1225, 149, 39, 118, 1161, 83, 715, 173, 45, 316, 93, 283, 60625, 9409, 801, 205, 261, 107, 11125 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Robert Israel, Table of n, a(n) for n = 2..719

EXAMPLE

a(6) = 55 = 9*6 +1 = 11*5 and 6 = 2*3 are both of prime signature p*q, where p and q are primes.

MAPLE

f:= proc(n) local k, s, p, best, q, r, x;

  s:= ps(n);

  if nops(s) = 1 then

     s:= s[1]; p:= 1; do p:= nextprime(p); if p^s mod n = 1 then return p^s fi od

  elif nops(s) = 2 then

    p:= 1; best:= infinity;

    do

      p:=nextprime(p);

      if n mod p = 0 then next fi;

      if 2^s[1]*p^s[2] > best then return best fi;

      if [msolve(x^s[1]*p^s[2]=1, n)]=[] then next fi;

      q:= 1;

      do

        q:= nextprime(q);

        if q = p or n mod q = 0 then next fi;

        r:= q^s[1]*p^s[2];

        if r > best then break fi;

        if r mod n = 1 then best:= r fi;

      od

    od

  fi;

  for k from 1 by n do if ps(k) = s then return k fi od

end proc:

map(f, [$1..100]); # Robert Israel, Mar 23 2021

PROG

(PARI) a(n) = my(ps = vecsort(factor(n)[, 2]), k = 1); while (vecsort(factor(k*n+1)[, 2]) != ps, k++); return (k*n+1); \\ Michel Marcus, Sep 15 2013; corrected Jun 14 2022

CROSSREFS

Second column of A113031.

Sequence in context: A338712 A263926 A114788 * A175637 A110404 A190366

Adjacent sequences:  A085071 A085072 A085073 * A085075 A085076 A085077

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jul 01 2003

EXTENSIONS

More terms from David Wasserman, Jan 12 2005

STATUS

approved

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Last modified July 2 18:27 EDT 2022. Contains 355029 sequences. (Running on oeis4.)