A323427 -id:A323427 - cp's OEIS frontend

A089374 Numbers n such that the concatenation (in descending order) of all the divisors of n, with 1 in the least significant position, is prime (or 1).

1, 3, 4, 7, 13, 19, 25, 31, 39, 43, 48, 91, 97, 103, 109, 117, 151, 157, 181, 193, 211, 241, 244, 247, 271, 289, 292, 301, 309, 325, 337, 349, 367, 388, 409, 421, 439, 487, 523, 547, 571, 597, 601, 613, 628, 631, 633, 687, 691, 703, 711, 733, 769, 772, 793, 811

Offset: 1

Amarnath Murthy, Nov 08 2003

See A176558(n) = reverse concatenation of divisors of n. See A175355 for corresponding values of reverse concatenations. Complement of A175354(n) for n >= 2. - Jaroslav Krizek, Apr 20 2010

If prime p divides n, then the exponent of p in the prime factorization of n is odd if p == 1 (mod 3) and even if p == 2 (mod 3). In particular, the sequence has no terms == 2 (mod 3). - Robert Israel, Apr 21 2020

			4 is a term as 421 is prime; 39 is a term as concatenation of 39,13,3 and 1, i.e. 391331, is prime.
25 is a member as 2551 is prime.
Divisors of 39 are 1,3,13,39; reverse concatenation of divisors 391331 is prime.
48 is a member as 48241612864321 is a prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A069582, A323427 (primes p such that p^2 is in the sequence).

select(n->isprime(parse(cat("",op(sort([op(numtheory[divisors](n))],`>`))))),[$1..3000])[]; (Alec Mihailovs, Aug 14 2005)

Join[{1},Select[Range[1000],PrimeQ[FromDigits[Flatten[IntegerDigits/@Reverse[Divisors[ #]]]]]&]] (* Harvey P. Dale, Feb 11 2024 *)

Corrected and extended by David Wasserman, Sep 15 2005

Edited by N. J. A. Sloane, Apr 29 2007, Aug 14 2010

A323428 Primes p such that the concatenation of p^3, p^2, p and 1 is prime.

Original entry on oeis.org

37, 79, 967, 3181, 3463, 3607, 3643, 3691, 3931, 4657, 5227, 5419, 5569, 5953, 6217, 6379, 6529, 7417, 7603, 7753, 7759, 8527, 8887, 9049, 9277, 9343, 9679, 9829, 9871, 31723, 32323, 32983, 33151, 33601, 34039, 35227, 36529, 36913, 37189, 38329, 38707, 38749, 39097, 40123, 41149, 41479, 42073

Offset: 1

J. M. Bergot and Robert Israel, Jan 14 2019

All terms == 1 (mod 6).

			a(3)=967 is a term because 967 is prime and 9042310639350899671 is prime, where 967^3=904231063 and 967^2=935089.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A323427.

cat4:= proc(x) local t;
  t:= 10*x+1;
  t:= x^2*10^(1+ilog10(t))+t;
  x^3*10^(1+ilog10(t))+t;
end proc:
select(t -> isprime(t) and isprime(cat4(t)), [seq(i,i=1..10^5,6)]);

pppQ[n_]:=PrimeQ[FromDigits[IntegerDigits/@Join[n^3, n^2, n, 1]]]; Select[Prime[Range[4500]], pppQ] (* Vincenzo Librandi, Jan 15 2019 *)

cp's OEIS Frontend

A089374 Numbers n such that the concatenation (in descending order) of all the divisors of n, with 1 in the least significant position, is prime (or 1).

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