A246754 Least positive number k such that k^k is at least 10^n digits long.

1, 10, 57, 387, 2890, 22934, 189482, 1611056, 13993960, 123579654, 1105747503, 10000000000, 91239358932, 838673386122, 7758099162327, 72158973089377, 674359248152535, 6328590417713813, 59611349660814244, 563355446524384647, 5339735395113038337

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = ceiling(exp(W(10^n*log(10)))) for n > 0. - Charles R Greathouse IV, Nov 16 2014

Prog

(PARI) a(n)= k=floor(sqrt(10^n)); while(#digits(k^k)<10^n, k++); k
n=0; while(n<10, print1(a(n), ", "); n++)
(PARI) a(n)=if(n, ceil(exp(lambertw(10^n*log(10)))), 1) \\ Charles R Greathouse IV, Nov 16 2014

Crossrefs

Sequence in context: A004142 A006529 A337001 * A024133 A229074 A103417

Adjacent sequences: A246751 A246752 A246753 * A246755 A246756 A246757

Keyword

nonn,base

Author

Derek Orr, Nov 15 2014

Extensions

More terms from Alois P. Heinz, Nov 15 2014

Status

approved