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.
27 is in the sequence because a single-digit number is reached in 3 iterations: 7^2 = 49, 9^4 = 6561, ((1^6)^5)^6 = 1, so A175424(27) = 3.
The only prime concatenations of the first n primes for n = 1..3 are a(1)=2, a(2)=23, and a(3)=523. For n=4, the only prime concatenations of 2, 3, 5, and 7 are 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523; the largest of these is a(4) = 7523.
from sympy import sieve, isprime
from itertools import permutations
for n in range(1, 14):
sieve.extend_to_no(n)
p = list(map(str, list(sieve._list)))[:n]
mint = 0
for i in permutations(p, len(p)):
t = int(''.join(i))
if t > mint and isprime(t):
mint = t
print(mint, end = ', ') # Gleb Ivanov, Dec 05 2021
The only prime concatenations of the first n primes for n = 1..3 are a(1)=2, a(2)=23, and a(3)=523. For n=4, the only prime concatenations of 2, 3, 5, and 7 are 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523; the smallest of these is a(4) = 2357.
from sympy import sieve, isprime
from itertools import permutations
for n in range(1, 20):
sieve.extend_to_no(n)
p = list(map(str, list(sieve._list)))[:n]
mint = 10**1000
for i in permutations(p, len(p)):
t = int(''.join(i))
if t < mint and isprime(t):
mint = t
if mint == 10**1000:
print(0, end = ', ')
else:
print(mint, end = ', ') # Gleb Ivanov, Dec 04 2021
a(2) = 4 because for the first 4 numbers {1,2,3,4} we have 1423, 2143, 2341, 4231 that are prime.
with(combinat): P:=proc(q) local a,b,j,k,n,t; a:=[]; for n from 1 to q do a:=permute(3*n-2); t:=0; for k from 1 to nops(a) do b:=0; for j from 1 to nops(a[k]) do b:=10^(ilog10(a[k][j])+1)*b+a[k][j]; od; if isprime(b) then t:=t+1; fi; od; print(t); od; end: P(5); # Paolo P. Lava, Nov 17 2017
Array[Count[Map[FromDigits@ Flatten[IntegerDigits@ #] &, Permutations[Range@ #, {#}]], ?PrimeQ] &, 10] (* _Michael De Vlieger, Nov 17 2017 *)
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