A346203 a(n) is the smallest nonnegative number k such that the decimal expansion of the product of the first k primes contains the string n.

3, 0, 1, 3, 10, 7, 2, 9, 9, 8, 4, 18, 17, 11, 15, 16, 14, 18, 24, 16, 11, 4, 9, 5, 21, 13, 13, 13, 9, 21, 3, 5, 10, 14, 12, 13, 26, 24, 12, 17, 18, 15, 12, 26, 16, 22, 10, 16, 12, 11, 13, 7, 13, 20, 17, 19, 11, 20, 15, 18, 11, 14, 21, 13, 10, 24, 20, 14, 21, 8, 9

Offset

0,1

Links

Table of n, a(n) for n=0..70.

Ilya Gutkovskiy, Scatterplot of a(n) up to n=100000

Index entries for sequences related to primorial numbers

Example

a(5) = 7 since 5 occurs in prime(7)# = 2 * 3 * 5 * 7 * 11 * 13 * 17 = 510510, but not in prime(0)#, prime(1)#, prime(2)#, ..., prime(6)#.

Mathematica

primorial[n_] := Product[Prime[j], {j, 1, n}]; a[n_] := (k = 0; While[! MatchQ[IntegerDigits[primorial[k]], {___, Sequence @@ IntegerDigits[n], ___}], k++]; k); Table[a[n], {n, 0, 70}]

Prog

(Python)
from sympy import nextprime
def A346203(n):
    m, k, p, s = 1, 0, 1, str(n)
    while s not in str(m):
        k += 1
        p = nextprime(p)
        m *= p
    return k # Chai Wah Wu, Jul 12 2021
(PARI) a(n) = my(k=0, p=1, q=1, sn=Str(n)); while (#strsplit(Str(q), sn)==1, k++; p=nextprime(p+1); q*=p); k; \\ Michel Marcus, Jul 13 2021; corrected Jun 15 2022

Crossrefs

Cf. A002110, A030000, A062584, A082058, A346120.

Sequence in context: A083857 A353077 A115142 * A327126 A273083 A307451

Adjacent sequences: A346200 A346201 A346202 * A346204 A346205 A346206

Keyword

nonn,base

Author

Ilya Gutkovskiy, Jul 10 2021

Status

approved