A380725 - OEIS

%I #41 Feb 18 2025 15:35:17

%S 1,13,22,31,40,108,117,126,135,144,153,162,171,180,207,216,225,234,

%T 243,252,261,270,306,315,324,333,342,351,360,405,414,423,432,441,450,

%U 504,513,522,531,540,603,612,621,630,702,711,720,801,810,900,1069,1078,1087,1096,1159,1168,1177,1186,1195

%N Positive integers k whose sum of digits equals the square of their number of digits.

%C This is a finite sequence since if k is L digits long then its sum of digits is at most 9*L which is < L^2 for L > 9.

%H Anwar Hahj Jefferson-George, <a href="/A380725/b380725.txt">Table of n, a(n) for n = 1..74583</a>

%t Select[Range[1200],DigitSum[#]==IntegerLength[#]^2&] (* _James C. McMahon_, Feb 18 2025 *)

%o (Rust)

%o /// Is the term a valid entry in a380725

%o pub fn a380725_predicate(mut k: usize) -> bool {

%o     let base = 10usize;

%o     let mut len = 0usize;

%o     let mut digit_sum = 0usize;

%o     while k > 0 {

%o         let digit = k.rem_euclid(base);

%o         k /= base;

%o         digit_sum += digit;

%o         len += 1;

%o     }

%o     digit_sum == len.pow(2u32)

%o }

%o (PARI) isok(k) = my(d=digits(k)); vecsum(d) == sqr(#d); \\ _Michel Marcus_, Feb 08 2025

%o (Python)

%o def ok(n): return sum(map(int, s:=str(n))) == len(s)**2

%o print([k for k in range(2000) if ok(k)]) # _Michael S. Branicky_, Feb 08 2025

%Y Cf. A007953 (sum of digits), A061384.

%K nonn,base,fini,full,easy,new

%O 1,2

%A _Anwar Hahj Jefferson-George_, Jan 30 2025