A380199 Smallest number of leading digits of A002110(n) (primorial(n)) that form a prime (or 0 if none exist).
0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 4, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 26, 3, 1, 1, 1, 4, 7, 1, 1, 3, 2, 1, 1, 17, 1, 2, 2, 6, 0, 1, 0, 25, 2, 2, 1, 3, 1, 21, 1, 32, 2, 2, 2, 25, 1, 1, 1, 0, 1, 10, 9, 2, 0, 1, 3, 0, 0, 17, 1, 6
Offset: 0
Examples
For n = 2, primorial(2) = 6, 6 is not prime, a(2) = 0. For n = 10, primorial(10) = 6469693230, 6469 is the smallest prime, a(10) = 4. n primorial(n) a(n) 0 1 0 1 2 1 2 6 0 3 30 1 4 210 1 5 2310 1 6 30030 1 7 510510 1 8 9699690 0 9 223092870 1 10 6469693230 4
Links
- Jean-Marc Rebert, Table of n, a(n) for n = 0..304
Programs
-
Mathematica
lim=84;p=FoldList[Times, 1, Prime[Range[lim]]];Table[l=Length[IntegerDigits[p[[n]]]];a=0;Do[If[PrimeQ[FromDigits[Take[IntegerDigits[p[[n]]],i]]],a=i;Break[]],{i,l}];a,{n,lim}] (* James C. McMahon, Jan 29 2025 *) -
PARI
a(n) = my(d=digits(factorback(primes(n)))); for(k=1, #d, if (isprime(fromdigits(Vec(d, k))), return(k))); return (0); \\ Michel Marcus, Jan 19 2025