A346203 - OEIS

%I #17 Jun 15 2022 10:49:14

%S 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,

%T 13,9,21,3,5,10,14,12,13,26,24,12,17,18,15,12,26,16,22,10,16,12,11,13,

%U 7,13,20,17,19,11,20,15,18,11,14,21,13,10,24,20,14,21,8,9

%N 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.

%H Ilya Gutkovskiy, <a href="/A346203/a346203.jpg">Scatterplot of a(n) up to n=100000</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%e 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)#.

%t 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}]

%o (Python)

%o from sympy import nextprime

%o def A346203(n):

%o     m, k, p, s = 1, 0, 1, str(n)

%o     while s not in str(m):

%o         k += 1

%o         p = nextprime(p)

%o         m *= p

%o     return k # _Chai Wah Wu_, Jul 12 2021

%o (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

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

%K nonn,base

%O 0,1

%A _Ilya Gutkovskiy_, Jul 10 2021