A272208 Numbers n such that n immediately follows the decimal point in the base-10 representation of sqrt(n).

8, 77, 5711, 9797, 997997, 8053139, 60755907, 99979997, 9999799997, 71515443427, 93445113269, 999997999997, 26369408771424, 96872443448748, 99650905131203, 99999979999997, 751273714618266, 3368237924952647, 3493498117381256, 9999999799999997, 35399255736521405, 999999997999999997

Offset: 1

Author

David W. Wilson, May 15 2016

Keywords

• nonn
• base
• hard

Comments

Sequence includes all numbers of form (10^n-3)(10^n+1) for n >= 1, hence is infinite.

Examples

			5711 immediately follows the decimal in sqrt(5711) = 75.5711+, so 5711 is in the sequence.
77327 does not immediately follow the decimal in sqrt(77327) = 278.077327+, so 77327 is not in this sequence.
		

Links

• David W. Wilson, Table of n, a(n) for n = 1..27

Crossrefs

Strict subsequence of A074841.

Programs

PARI

is(n)=my(t=10^#Str(n)); sqrtint(t^2*n)%t==n \\ Charles R Greathouse IV, May 16 2016