A143578 -id:A143578 - cp's OEIS frontend

A142591 Composite terms in A143578.

15, 35, 95, 119, 143, 209, 287, 319, 323, 377, 527, 559, 779, 899, 923, 989, 1007, 1189, 1199, 1343, 1349, 1763, 1919, 2159, 2507, 2759, 2911, 3239, 3599, 3827, 4031, 4607, 5183, 5207, 5249, 5459, 5543, 6439, 6887, 7067, 7279, 7739, 8159, 8639, 9179, 9593

Offset: 1

Leroy Quet, Aug 24 2008

nonn

Conjecture: This consists exactly of the semiprimes p*q for which p + q divides p*q + 1. - Mohamed Bouhamida, Aug 17 2009 (Comment edited by N. J. A. Sloane, Sep 01 2019.)

Robert Israel, Table of n, a(n) for n = 1..2100

Cf. A143578.

filter:= proc(n) local k,D,j,t;
  D:= select(t -> t^2 <= n, numtheory:-divisors(n));
  j:= max(D);
  t:= j+n/j;
  andmap(k -> (k+n/k) mod t = 0, D);
end proc:
count:= 0: S:= NULL:
for n from 2  while count < 100 do
  if  isprime(n) then next
  elif filter(n) then
    count:= count+1;
    S:= S, n;
  fi
od:
S; # Robert Israel, Sep 01 2019

Select[Reap[Module[{n, k}, For[n = 1, n < 10000, n++, k = Max[Select[Divisors[n], # <= Sqrt[n]&]]; If[Length[Union[ Mod[Divisors[n] + n/Divisors[n], k+n/k]]] == 1, Sow[n]]]]][[2, 1]], CompositeQ] (* Jean-François Alcover, Feb 07 2023 *)

More terms from M. F. Hasler, Aug 25 2008

a(33)-a(46) from Ray Chandler, Jun 21 2009

A235480 Primes whose base-3 representation is also the base-9 representation of a prime.

Original entry on oeis.org

2, 5, 7, 11, 17, 19, 23, 31, 37, 41, 43, 53, 67, 71, 73, 83, 89, 97, 103, 149, 157, 199, 239, 251, 257, 271, 277, 293, 307, 313, 331, 337, 359, 383, 397, 421, 431, 433, 499, 541, 557, 571, 587, 599, 601, 613, 631, 653, 659, 661, 683, 691, 709, 727, 751, 769, 823, 887, 911, 983, 1009, 1021, 1031, 1049, 1051, 1063, 1129, 1163, 1217

Offset: 1

M. F. Hasler, Jan 12 2014

This sequence is part of a two-dimensional array of sequences, given in the LINK, based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.

Appears to be a subsequence of A015919, A045344, A052085, A064555 and A143578.

			5 = 12_3 and 12_9 = 11 are both prime, so 5 is a term.

Giovanni Resta, Table of n, a(n) for n = 1..10000
M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Cf. A235265, A235473 - A235479, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.

Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 3], 9] &] (* Giovanni Resta, Sep 12 2019 *)

is(p,b=9,c=3)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: Code only valid for b > c.

cp's OEIS Frontend

A142591 Composite terms in A143578.

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