A046030 Numbers whose digits are squares.

0, 1, 4, 9, 10, 11, 14, 19, 40, 41, 44, 49, 90, 91, 94, 99, 100, 101, 104, 109, 110, 111, 114, 119, 140, 141, 144, 149, 190, 191, 194, 199, 400, 401, 404, 409, 410, 411, 414, 419, 440, 441, 444, 449, 490, 491, 494, 499, 900, 901, 904, 909, 910, 911, 914, 919

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1001
• Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
• Eric Weisstein's World of Mathematics, Smarandache Sequences.

Programs

Magma

[n: n in [0..1000] | forall{d: d in Intseq(n) | d in [0,1,4,9]}]; // Bruno Berselli, Jan 10 2013

Mathematica

Union[FromDigits/@Flatten[With[{l={0,1,4,9}},Table[Tuples[l,{i}],{i,3}]],1]]  (* Harvey P. Dale, Dec 19 2010 *)
Select[Range[0, 999], Intersection[{2, 3, 5, 6, 7, 8}, Union[IntegerDigits[#]]] == {} &] (* T. D. Noe, Dec 20 2010 *)

PARI

is(n)=#setintersect(Set(digits(n)), [2,3,5,6,7,8])==0 \\ Charles R Greathouse IV, Feb 11 2017

Formula

Sum_{n>=2} 1/a(n) = 2.105050135115910443669713125834050962799269137280589957713644901011872709688... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 15 2024

Extensions

Offset corrected by Amiram Eldar, Feb 15 2024