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

Author

Amarnath Murthy, Mar 10 2002

Keywords

• nonn
• base

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.

Examples

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

References

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

Crossrefs

Cf. A068844.

Programs

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 *)

Extensions

More terms from Sascha Kurz, Mar 17 2002