A159547 Smallest number b such that the number whose digits are n in base b is a skinny number.

2, 5, 10, 17, 26, 37, 50, 65, 82, 2, 3, 5, 10, 17, 26, 37, 50, 65, 82, 5, 5, 9, 13, 17, 26, 37, 50, 65, 82, 10, 10, 13, 19, 25, 31, 37, 50, 65, 82, 17, 17, 17, 25, 33, 41, 49, 57, 65, 82, 26, 26, 26, 31, 41, 51, 61, 71, 81, 91, 37, 37, 37, 37, 49, 61, 73, 85, 97, 109

Offset: 1

Author

J. Lowell, Apr 14 2009

Keywords

• nonn
• base

Comments

I assume that "the number whose digits are n in base b" means the number Sum c_i b^i, where the decimal expansion of n is Sum c_i 10^i. - N. J. A. Sloane, Jun 19 2021

Examples

			a(10) = 2 because 10^2 = 100 in all bases >= 2.
a(14) = 17 because 14_16 = 20_10, so the square is 400_10 = (1,9,0)_16, but digitsum((1,9,0)_16) = 10 != digitsum((1,4)_16)^2; while in base 17, 14_17 = 21_10, so the square is 441_10 = (1,8,16)_17 and digitsum((1,8,16)_17) = 25 = digitsum((1,4)_17)^2.
		

Crossrefs

Cf. A061909.

Programs

PARI

a(n) = my(d=digits(n), s); s=vecsum(d); for(b=1+vecmax(d), oo, if(s^2==sumdigits(fromdigits(d, b)^2, b), return(b))); \\ Jinyuan Wang, Jun 19 2021

Formula

a(n) <= 10 iff n is in A061909.

Extensions

More terms from Jinyuan Wang, Jun 19 2021