A068845 Final digits of the smallest prime starting with n!.

1, 3, 1, 1, 1, 7, 1, 29, 17, 43, 29, 13, 47, 19, 73, 37, 19, 41, 31, 41, 31, 1, 1, 37, 31, 37, 59, 41, 53, 41, 47, 1, 1, 89, 37, 53, 73, 1, 1, 43, 151, 1, 47, 1, 509, 127, 71, 167, 67, 167, 149, 67, 61, 139, 67, 59, 107, 241, 1, 61, 1, 149, 293, 127, 71, 151, 337, 107, 1

Offset

1,2

Comments

a(n)= 1 or a(n) >= the smallest prime larger than n. Conjecture: The terms are noncomposite numbers. Motivation: a composite number not coprime to n! cannot be a member.

References

Amarnath Murthy, Smarandache Reciprocal function and an elementary inequality. Smarandache Notions Journal, Vol. 1-2-3, Spring 2000.

Links

Table of n, a(n) for n=1..69.

Example

a(7) = 11 because the smallest prime starting with 7! = 5040 is 504011 and so the last digits are 11.

Maple

for i from 1 to 70 do a := nextprime(i!*10); b := 1; while(a-i!*10^b>=10^b) do b := b+1; a := nextprime(i!*10^b); end do; c[i] := a-i!*10^b; end do:q := seq(c[i], i=1..70);

Mathematica

Table[p = i!; k = 1; While[IntegerDigits[p] != Take[IntegerDigits[x = NextPrime[y = p*10^k]], IntegerLength[p]], k += 1]; x - y, {i, 69}] (* Jayanta Basu, Aug 09 2013 *)

Crossrefs

Cf. A068844.

Sequence in context: A293682 A276651 A185587 * A324910 A257100 A152884

Adjacent sequences: A068842 A068843 A068844 * A068846 A068847 A068848

Keyword

nonn,base

Author

Amarnath Murthy, Mar 10 2002

Extensions

More terms from Sascha Kurz, Mar 17 2002

Status

approved