OFFSET
1,1
COMMENTS
Here, intertwine means each prime is consecutively placed between each pair of digits. So, the prime a(n) should have n+1 digits. - Michael S. Branicky, Sep 10 2025
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..625
Chris K. Caldwell and G. L. Honaker, Jr., 1000000087, Prime Curios!.
FORMULA
a(n) = min_{p prime = d0 d1 .. dn} such that d0 p1 d1 p2 .. pn dn is prime, where di are single digits and pi = prime(i). - Michael S. Branicky, Sep 10 2025
EXAMPLE
a(5) = 100003 because it is the first 6-digit prime and if we intertwine each of its digits with the sequence of the first 5 primes, we obtain prime 120305070113 (1-2-0-3-0-5-0-7-0-11-3).
MATHEMATICA
f[n_]:=NestWhile[NextPrime, 10^n, ! PrimeQ[FromDigits[Flatten[IntegerDigits /@
Riffle[IntegerDigits@#, Prime@Range@n]]]] &]; Table[f[n], {n, 20}]
PROG
(Python)
from sympy import isprime, nextprime
def ok(n):
if n < 10: return False
s, p, t = str(n), 2, ""
for i in range(len(s)-1): t, p = t + s[i] + str(p), nextprime(p)
return isprime(int(t+s[-1]))
def a(n):
p = nextprime(10**n)
while not ok(p): p = nextprime(p)
return p
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Sep 09 2025
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Zhining Yang, Sep 09 2025
STATUS
approved
