A293832 Smallest of a run of n consecutive integers in A061910, i.e., for which the sum of digits of their square is again a square.
1, 1, 1, 9, 9, 9, 9, 46045846, 302260461719025
Offset: 1
Examples
For k = 1, 2 and 3, k^2 is a single-digit number and thus equal to its sum of digits, which therefore is a square. Therefore a(n) = 1 starts the first run of n consecutive integers with this property, for n = 1, 2 and 3.
However, the square of k = 4 has digit sum 7 which is not a square, and the same is the case for k = 5, 7 and 8. (Only k = 6 would have the required property.)
The consecutive integers { 9, 10, 11, 12, 13, 14, 15 } have squares 81, 100, 121, 169, 196, 225 which all have a digit sum (9, 1, 4, 16, 16 and 9) which is a square. Therefore a(n) = 9 starts the first run of n consecutive integers with this property, for n = 4 through 7.
(Actually, 10^(3m-2)^2-1 starts a run of 7 such numbers, for any m >= 1.)
The first run of 8 such numbers is (46045846, ..., 46045853), whence a(8) = 46045846.
Links
- User 'mathlove', Numbers n such that the digit sum of n^2 is a square, Mathematics StackExchange, Jan. 6, 2015.
Programs
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PARI
A293832(n,k=0)=until(,forstep(j=n,1,-1,issquare(sumdigits((k+j)^2))||next(2+!k+=j));return(k+1))
Extensions
a(9) from Giovanni Resta, Aug 27 2018
Comments