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URL: https://oeis.org/A390378

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A390378
a(n) is the smallest k > n such that prime(k)# contains the digits of prime(n)# as a substring.
1
4, 4, 8, 6, 13, 74, 295, 842, 2848, 9267, 73858, 481646
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Primorial.
EXAMPLE
a(4) = 13 since prime(4)# = 210 and prime(13)# = 304250263527210.
MATHEMATICA
primorial[n_] := Product[Prime[j], {j, n}]; Table[k = n + 1; While[Length@SequencePosition[IntegerDigits[primorial[k]], IntegerDigits[primorial[n]]] == 0, k++]; k, {n, 0, 9}]
PROG
(PARI) P(n) = vecprod(primes(n));
a(n) = my(k=n+1, sp=Str(P(n))); while (#strsplit(Str(P(k)), sp) < 2, k++); k; \\ Michel Marcus, Dec 18 2025
(Python)
from itertools import count
from gmpy2 import mpz, digits, next_prime
from sympy import primorial, prime
def A390378(n):
if n == 0: return 4
m = mpz(primorial(n))
p = prime(n+1)
s = digits(m)
for k in count(n+1):
m *= p
if s in digits(m):
return k
p = next_prime(p) # Chai Wah Wu, Dec 22 2025
CROSSREFS
KEYWORD
nonn,base,hard,more
AUTHOR
Ilya Gutkovskiy, Dec 16 2025
EXTENSIONS
a(10)-a(11) from Michael S. Branicky, Dec 18 2025
STATUS
approved