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.
c(1) = 1 not prime -> 1 is not a term. c(2) = 2 prime -> 2 is a term. c(3) = 3 prime -> 3 is a term. c(4) = 22 not prime -> 4 is not a term. c(5) = 5 prime -> 5 is a term. c(6) = 23 prime -> 6 is a term.
q:= n-> isprime(parse(cat(sort(map(i-> i[1]$i[2], ifactors(n)[2]))[]))): select(q, [$2..222])[]; # Alois P. Heinz, Mar 27 2024
m[{p_, e_}] := Table[p, {e}]; c[w_] := FromDigits[Join @@ IntegerDigits@ w]; Select[ Range@ 150, PrimeQ@ c@ Flatten[m /@ FactorInteger[#]] &] (* Giovanni Resta, Apr 23 2021 *)
from sympy import *
def b(n):
f=factorint(n)
l=sorted(f)
return 1 if n==1 else int("".join(str(i)*f[i] for i in l))
# print([b(n) for n in range(1, 101)])
for n in range(1,200):
if isprime(b(n)):
print (n)
95 = 5*19 -> 519 = 3*173 -> 3173 = 19*167 -> 19167 = 3*6389 and 36389 is prime.
filter:= proc(n) local k,F,x,j;
x:= n;
for k from 1 to 4 do
if isprime(x) then return false fi;
F:= sort(ifactors(x)[2],(a,b) -> a[1] t[1] $ t[2], F);
x:= F[1];
for j from 2 to nops(F) do
x:= x*10^(1+ilog10(F[j]))+F[j]
od;
od;
isprime(x)
end proc:
select(filter, [$2..1000]);# Robert Israel, Jun 25 2019
\\ See Links section.
698 is in the sequence as 698 -> 2349 -> 333329 -> 2571297 -> 3857099 -> 31312323 -> 33771937101 -> 379437170413 -> 73124171910091 -> 374148203145623. Only after the ninth iteration we reach a prime. - _David A. Corneth_, Oct 15 2019
is(n, k) = if(isprime(n), return(0)); for(i = 1, k - 1, n = concatelements(primesvector(n)); if(isprime(n), return(0))); n = concatelements(primesvector(n)); isprime(n) concatelements(v) = my(s = ""); for(i = 1, #v, s = concat(s, v[i])); eval(s) primesvector(n) = my(f = factor(n), res = vector(vecsum(f[,2])), t = 0); for(i = 1, #f~, for(j = 1, f[i, 2], t++; res[t] = f[i, 1])); res \\ David A. Corneth, Oct 15 2019
Prime factors of 140 are 2, 5, and 7 and 257 is prime, so 140 is a term.
Select[Range[220],Length[x=First/@FactorInteger[#]]>1&&PrimeQ[FromDigits[Flatten[IntegerDigits[x]]]]&]
from sympy import isprime, primefactors
def ok(n):
pf = primefactors(n)
if len(pf) < 2: return False
return isprime(int("".join(str(p) for p in pf)))
print(list(filter(ok, range(2, 220)))) # Michael S. Branicky, Jun 12 2021
24 = 2*2*2*3, 2223 = 3*3*13*19, 331319 is prime.
69 = 3*23 -> 323 = 17*19 -> 1719 = 3*3*191 and 33191 is prime.
14 = 2*7 -> 27 = 3*3*3 -> 333 = 3*3*37 -> 3337 = 47*71 -> 4771 = 13*367 and 13367 is prime.