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

0,11

Links

Jean-Marc Rebert, Table of n, a(n) for n = 0..304

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000040, A002110, A379944.

Sequence in context: A039927 A336722 A073802 * A132157 A103163 A128211

Adjacent sequences: A380196 A380197 A380198 * A380200 A380201 A380202

Keyword

nonn,base

Author

Jean-Marc Rebert, Jan 16 2025

Status

approved