A357894 Integers k such that the sum of some number of initial decimal digits of sqrt(k) is equal to k.

0, 1, 6, 10, 14, 18, 27, 33, 41, 43, 46, 55, 56, 62, 66, 69, 70, 77, 80, 87, 93, 98, 102, 108, 110, 123, 124, 145, 147, 149, 150, 154, 157, 162, 164, 165, 168, 176, 177, 179, 180, 182, 183, 197, 204, 213, 214, 219, 224, 236, 237, 242, 248, 251, 252, 261, 262, 263, 271, 274, 285, 295

Offset: 1

Author

Gil Broussard, Oct 18 2022

Keywords

• nonn
• base

Comments

For integers k that are squares of integers, "Sum of initial digits" includes digits to the left of the decimal point only, as there are no digits other than zero to the right of the decimal point. This constraint contributes terms 0 and 1 to the sequence.

For integers k with irrational sqrt(k), "Sum of initial digits" includes digits to the left of the decimal point and to the right of the decimal point.

"Initial digits" implies a sufficient number of digits to produce either a sum > k or a sum = k condition, halting at whichever condition occurs first (sum > k condition is discarded).

Examples

			41 is a term because sqrt(41) = 6.4031242374328... and 6+4+0+3+1+2+4+2+3+7+4+3+2 = 41.
42 is not a term because sqrt(42) = 6.480740698407860... and 6+4+8+0+7+4+0+6 = 35 and 6+4+8+0+7+4+0+6+9 = 44 (no sum of initial digits = 42).
144 is not a term because sqrt(144) = 12 (no digits to the right of the decimal), and 1+2 is not equal to 144.
		

Crossrefs

Cf. A106039.

Programs

PARI

is(n) = { my (d=digits(sqrtint(n)), s=0); for (i=1, #d, s+=d[i]; if (s==n, return (1), s>n, return (0););); if (issquare(n), return (n==0);); my (n0=n); while (1, s+=sqrtint(n0*=100)%10; if (s==n, return (1), s>n, return (0););); } \\ Rémy Sigrist, Oct 19 2022