A111347 -id:A111347 - cp's OEIS frontend

A111348 Numbers n such that the result of swapping the 3rd and next to the next to the last digit of a number is prime.

101, 104, 106, 107, 110, 112, 113, 118, 119, 124, 125, 128, 130, 131, 133, 134, 136, 140, 142, 145, 146, 149, 151, 152, 157, 160, 164, 166, 167, 170, 172, 175, 179, 181, 182, 188, 191, 194, 196, 199, 200, 300, 301, 305, 310, 311, 313, 316, 320, 322, 325

Offset: 1

Cino Hilliard, Nov 05 2005

Similar to A095179 for the first few terms.

Since these numbers are just digit permutations of the primes the sequence is obviously infinite. - Charles R Greathouse IV, Oct 20 2008

Cf. A095179, A111347, A111349.

swapn(n,d) = \ d is the digit position to swap { local(j,ln,x,s,y,y2,tmp); for(x=10^(d-1),10^(d-1)+n, s = Str(x); ln = length(s); y = eval(Vec(s)); tmp=y[d]; y[d]=y[ln-d+1]; y[ln-d+1]=tmp; y2=0; for(j=1,ln, y2+=y[j]*10^(ln-j); ); if(isprime(y2),print1(x",")) ) }

For N1=a(n)*10^n+a(n-1)*10^(n-1)+a(n-2)*10^(n-2)+...+a(2)*10^2+a(1)*10 + a(0), N2=a(n)*10^n+a(n-1)*10^(n-1)+a(2)*10^(n-2)+...+a(n-2)*10^2+a(1)*10 + a(0) is prime.

A111349 Numbers n such that the result of swapping the 4th digit and the digit 3 positions from the last digit is prime.

Original entry on oeis.org

1003, 1004, 1007, 1009, 1010, 1012, 1013, 1015, 1016, 1018, 1019, 1021, 1024, 1025, 1030, 1031, 1040, 1043, 1049, 1051, 1054, 1055, 1060, 1061, 1063, 1070, 1082, 1085, 1088, 1091, 1094, 1096, 1099, 1100, 1105, 1106, 1108, 1112, 1114, 1118, 1123, 1126

Offset: 1

Cino Hilliard, Nov 05 2005

Leading zeros are dropped.

Since these numbers are just digit permutations of the primes the sequence is obviously infinite. - Charles R Greathouse IV, Oct 20 2008

Cf. A095179, A111347, A111348.

swapn(n,d) = \ d is the digit position to swap { local(j,ln,x,s,y,y2,tmp); for(x=10^(d-1),10^(d-1)+n, s = Str(x); ln = length(s); y = eval(Vec(s)); tmp=y[d]; y[d]=y[ln-d+1]; y[ln-d+1]=tmp; y2=0; for(j=1,ln, y2+=y[j]*10^(ln-j); ); if(isprime(y2),print1(x",")) ) }

A272022 Look at the set of numbers obtained by permuting the digits of n in all possible ways, then remove n itself from the set. If the remaining numbers are all primes, then n is in the sequence.

Original entry on oeis.org

13, 14, 16, 17, 20, 30, 31, 32, 34, 35, 37, 38, 50, 70, 71, 73, 74, 76, 79, 91, 92, 95, 97, 98, 110, 113, 118, 119, 131, 133, 199, 311, 337, 373, 733, 772, 775, 778, 779, 919, 991, 1118, 3337, 7771, 77779

Offset: 1

César Eliud Lozada, Apr 18 2016

If it exists, a(46) > 5*10^11. - Lars Blomberg, Mar 31 2018

			119 is in the sequence because every permutation of its digits excluding 119 (i.e., 191 and 911) is a prime.
11 is not in the sequence, because when 11 is removed from the set, no numbers are left.

Cf. A095179, A111347.

Cf. A003459. - Altug Alkan, Apr 18 2016

lis := [];
for n from 1 to 10000 do
  nn := convert(n, base, 10);
  pp := combinat[permute](nn);
  if nops(pp) = 1 then
    next
  end if;
  lOk := true;
  for p in pp do
    if p = nn then
      next: #exclude n
    end if;
    if `not`(isprime(convert(p, base, 10, 10^nops(p))[])) then
      lOk := false; break
    end if
  end do;
  if lOk then
    lis := [op(lis), n]
  end if
end do:
lis := lis;

rnapQ[n_]:=Module[{p=Rest[FromDigits/@Permutations[IntegerDigits[ n]]]},If[ Length[p]==0, False, AllTrue[p,PrimeQ]]]; Select[Range[80000],rnapQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 24 2019 *)

isok(n) = {v = []; d = digits(n); for (k=0, (#d)!-1, p = numtoperm(#d, k); dp = vector(#d, j, d[p[j]]); np = subst(Pol(dp), x, 10); v = Set(concat(v, np));); v = setminus(v, Set(n)); if (#v == 0, return (0)); for (k=1, #v, if (!isprime(v[k]), return (0));); return (1);} \\ Michel Marcus, Apr 18 2016

from sympy import isprime
from itertools import count, islice, permutations
def agen(): yield from (k for k in count(1) if len(set(s:=str(k)))!=1 and all((t:=int("".join(m)))==k or isprime(t) for m in permutations(s)))
print(list(islice(agen(), 45))) # Michael S. Branicky, Dec 29 2023

cp's OEIS Frontend

A111348 Numbers n such that the result of swapping the 3rd and next to the next to the last digit of a number is prime.

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A111349 Numbers n such that the result of swapping the 4th digit and the digit 3 positions from the last digit is prime.

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A272022 Look at the set of numbers obtained by permuting the digits of n in all possible ways, then remove n itself from the set. If the remaining numbers are all primes, then n is in the sequence.

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