A068840 Smallest prime with leading digits the same as those of n^n.

11, 41, 271, 25601, 31253, 466561, 8235431, 167772161, 3874204891, 100000000003, 2853116706113, 89161004482567, 3028751065922539, 111120068255580169, 437893890380859375031, 184467440737095516163, 82724026188633676417741, 3934640807529653757542407

Offset

1,1

Comments

Observation: In most cases only one extra digit is required.

The observation is increasingly inaccurate for large n, where it happens with 'probability' ~ 10/n log n. But a(n) always exists due to the prime number theorem. - Charles R Greathouse IV, Nov 19 2010

Links

Jayanta Basu, Table of n, a(n) for n = 1..50

Example

a(5) = 31253 because this is the smallest prime starting with 5^5 = 3125.

Maple

for i from 1 to 40 do a := nextprime(i^i*10); b := 1; while(a-i^i*10^b>=10^b) do b := b+1; a := nextprime(i^i*10^b); end do; c[i] := a; end do:q := seq(c[i], i=1..40);

Mathematica

Table[p = i^i; k = 1; While[IntegerDigits[p] != Take[IntegerDigits[x = NextPrime[p*10^k]], IntegerLength[p]], k += 1]; x, {i, 18}] (* Jayanta Basu, Aug 09 2013 *)

Crossrefs

Sequence in context: A333084 A201709 A092445 * A082424 A153173 A050526

Adjacent sequences: A068837 A068838 A068839 * A068841 A068842 A068843

Keyword

nonn,base

Author

Amarnath Murthy, Mar 10 2002

Extensions

More terms from Sascha Kurz, Mar 17 2002

Extended by Jayanta Basu, Aug 09 2013

Status

approved