This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
isok(n)={my(v=vecsort(digits(n))); if(#Set(v)<#v, 1, forperm(v, u, my(t=fromdigits(Vec(u))); if(isprime(t) && t<>n, return(1))); 0)} \\ Andrew Howroyd, Jan 22 2023
from sympy import isprime
from itertools import permutations as P
def ok(n):
if not isprime(n): return False
if len(s:=str(n)) > len(set(s)): return True
return any(isprime(t) for t in (int("".join(p)) for p in P(s)) if t!=n)
print([k for k in range(422) if ok(k)]) # Michael S. Branicky, Jan 23 2023
2, 3, 5, and 7 are excluded, since they have no two digits to exchange. 11 is excluded, since it yields only itself. 13 and 17 are included, since they yield the primes 31 and 71. 19, 23, and 29 are excluded, since they yield the composite numbers 91, 32, and 92.
filter:= proc(n) local L,d,i;
if not isprime(n) then return false fi;
L:= convert(n,base,10); d:= nops(L);
for i from 1 to d-1 do
if L[i] <> L[i+1] and isprime(n + (L[i]-L[i+1])*(10^i-10^(i-1))) then return true fi
od;
false
end proc:
select(filter, [seq(i,i=11 .. 1---,2)]); # Robert Israel, Sep 04 2024
Select[Prime[Range[100]], With[{digits = IntegerDigits[#]}, AnyTrue[Complement[FromDigits[Permute[digits, Cycles[{{#, # + 1}}]]] & /@ Range[Length[digits] - 1], {#}], PrimeQ]] &]
from sympy import isprime
def ok(n):
if not isprime(n): return False
s = str(n)
for i in range(len(s)-1):
t = int(s[:i]+s[i+1]+s[i]+s[i+2:])
if t != n and isprime(t): return True
return False
print([k for k in range(504) if ok(k)]) # Michael S. Branicky, Sep 04 2024
The first terms, alongside the corresponding other prime numbers, are:
n a(n) Other prime numbers
-- ---- -------------------
1 13 {31}
2 17 {71}
3 31 {13}
4 37 {73}
5 71 {17}
6 73 {37}
7 79 {97}
8 97 {79}
9 113 {131, 311}
10 127 {271}
11 131 {113, 311}
12 149 {491}
See Links section.
13 is the first term, since 31 is also prime. 113 is a term, since 131 is prime. 101 is not allowed as a term: 011 is prime, but has a leading zero.
from sympy import isprime
from itertools import combinations
def ok(n):
if not isprime(n): return False
s = list(str(n))
for i, j in combinations(range(len(s)), 2):
sij = s[:]
sij[i], sij[j] = sij[j], sij[i]
if sij[0] != "0" and sij != s and isprime(int("".join(sij))):
return True
return False
print([k for k in range(565) if ok(k)]) # Michael S. Branicky, Sep 07 2024
The first term is the prime 113, since 131 and 311 are also prime. Another term is 1013, since 1103 and 1301 are prime.
from sympy import isprime
from itertools import combinations, permutations
def ok(n):
if n < 100 or not isprime(n): return False
s = list(str(n))
for i, j, k in combinations(range(len(s)), 3):
pset, w, x = {n}, s[:], s[:]
w[i], w[j], w[k] = w[j], w[k], w[i]
x[i], x[j], x[k] = x[k], x[i], x[j]
if w[0] != "0" and isprime(t:=int("".join(w))): pset.add(t)
if x[0] != "0" and isprime(t:=int("".join(x))): pset.add(t)
if len(pset) == 3: return True
return False
print([k for k in range(1920) if ok(k)]) # Michael S. Branicky, Sep 17 2024
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