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

1,1

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

Links

Table of n, a(n) for n=1..69.

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A061909.

Sequence in context: A059591 A082607 A303372 * A002522 A217990 A322008

Adjacent sequences: A159544 A159545 A159546 * A159548 A159549 A159550

Keyword

nonn,base

Author

J. Lowell, Apr 14 2009

Extensions

More terms from Jinyuan Wang, Jun 19 2021

Status

approved