A120713 -id:A120713 - cp's OEIS frontend

A107374 Records in A120713.

2, 23, 37, 211, 311, 313, 317, 23691827, 236132639, 2711142277, 236918275481, 23671421424998147, 23611223366121242363, 27111422497798154539, 23611192233385766114209418627, 23611222333466669138253506759, 236918274154821232463697381107, 2361122333766741112224078141221

Offset: 1

N. J. A. Sloane, Jul 21 2007

nonn

A120716 a(1)=1, a(p)=p if p is a prime. Otherwise, start with n and iterate the map (k -> concatenation of nontrivial divisors of k) until we reach a prime q; then a(n) = q. If we never reach a prime, a(n) = -1.

Original entry on oeis.org

1, 2, 3, 2, 5, 23, 7

Offset: 1

N. J. A. Sloane, Jul 19 2007

a(8) is currently unknown.

The sequence continues from a(8)-a(100): >10^50, 3, 5, 11, >10^50, 13, 313, 1129, >10^50, 17, >10^50, 19, >10^50, 37, 211, 23, >10^50, 5, 3251, 313, >10^50, 29, >10^50, 31, >10^50, 311, >10^50, 1129, >10^50, 37, 373, 313, >10^50, 41, >10^50, 43, >10^50, >10^50, 223, 47, >10^50, 7, >10^50, 317, >10^50, 53, 23691827, 773, >10^50, 1129, 229, 59, >10^50, 61, >10^50, 378593, >10^50, >10^5", >10^50, 67, >10^50, 39191573, >10^50, 71, >10^50, 73, 379, >10^50, >10^50, 3979237, 236132639, 79, >10^50, >10^50, 241, 83, >10^50, 3137, >10^50, 3983249, >10^50, 89, >10^50, >10^50, >10^50, 331, 1319, 36389, >10^50, 97, >10^50, 391133, >10^50. - Robert Price, Mar 27 2019

			4 -> 2, prime, so a(4) = 2.
6 -> 2,3 -> 23, prime, so a(6) = 23.
8 -> 2,4 -> 24 -> 2,3,4,6,8,12 -> 2346812 -> 2,4,13,26,52,45131,90262,180524,586703,1173406 -> 2413265245131902621805245867031173406 -> ? (see link for the continuation)
9 -> 3, prime, so a(9) = 3.
21 -> 3,7 -> 37, prime, so a(21) = 37.

N. J. A. Sloane et al., Notes on the attempt to find a(8)

Cf. A120712, A120713, A037274, A037279, A130139 (a bisection), A130140, A130141, A130142.

A120716[n_] := Module[{x},
   If[n == 1, Return[1]];
   If[PrimeQ[n], Return[n]];
   x = FromDigits[Flatten[IntegerDigits[Rest[Most[Divisors[n]]]]]];
   If[x > 10^50, Return[">10^50"], A120716[x]]];
Table[A120716[n], {n, 1, 100}] (* Robert Price, Mar 27 2019 *)

Edited by Michel Marcus, Mar 09 2023

A120712 Numbers k with the property that the concatenation of the nontrivial divisors of k (i.e., excluding 1 and k) is a prime.

Original entry on oeis.org

4, 6, 9, 21, 22, 25, 33, 39, 46, 49, 51, 54, 58, 78, 82, 93, 99, 111, 115, 121, 133, 141, 142, 147, 153, 154, 159, 162, 166, 169, 174, 177, 186, 187, 189, 201, 205, 219, 226, 235, 237, 247, 249, 253, 262, 267, 274, 286, 289, 291, 294, 301, 318

Offset: 1

Eric Angelini, Jul 19 2007

			   k |    divisors    | concatenation
  ---+----------------+--------------
   4 | (1) 2      (4) |        2
   6 | (1) 2, 3   (6) |       23
   9 | (1) 3      (9) |        3
  21 | (1) 3, 7  (21) |       37
  22 | (1) 2, 11 (22) |      211
  25 | (1) 5     (25) |        5
  33 | (1) 3, 11 (33) |      311
  39 | (1) 3, 13 (39) |      313

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A037274, A037278, A037279, A106708, A120713, A120716.

Cf. A130139, A130140, A130141, A130142.

with(numtheory):
for k from 2 to 1000 do:
v0:=divisors(k):
nn:=nops(v0):
if nn > 2 then
v1:=[seq(v0[j],j=2..nn-1)]:
v2:=cat(seq(convert(v1[n],string),n=1..nops(v1))):
v3:=parse(v2):
if isprime(v3) = true then lprint(k,v3) fi:
fi:
od: # Simon Plouffe

fQ[n_] := PrimeQ@ FromDigits@ Most@ Rest@ Divisors@ n; Select[ Range[2, 320], fQ]

from sympy import divisors, isprime
def ok(n):
    s = "".join(str(d) for d in divisors(n)[1:-1])
    return s != "" and isprime(int(s))
print([k for k in range(319) if ok(k)]) # Michael S. Branicky, Oct 01 2024

Name edited by Michel Marcus, Mar 09 2023

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A107374 Records in A120713.

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A120716 a(1)=1, a(p)=p if p is a prime. Otherwise, start with n and iterate the map (k -> concatenation of nontrivial divisors of k) until we reach a prime q; then a(n) = q. If we never reach a prime, a(n) = -1.

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A120712 Numbers k with the property that the concatenation of the nontrivial divisors of k (i.e., excluding 1 and k) is a prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Python

Extensions