A166550 Numbers n with property that n^2 and n-th prime have the same sum of digits.

4, 8, 11, 22, 34, 59, 61, 85, 179, 229, 260, 266, 352, 385, 391, 403, 418, 440, 491, 565, 595, 619, 724, 770, 832, 844, 961, 965, 980, 1012, 1039, 1069, 1075, 1099, 1108, 1127, 1139, 1148, 1211, 1217, 1390, 1468, 1585, 1589, 1649, 1747, 1780, 1789, 1795, 1799

Offset: 1

Author

Zak Seidov, Oct 16 2009

Keywords

• base
• nonn

Comments

A007605(n)=A004159(n).

Examples

			4^2=16, prime(4)=7, 1+6=7
8^2=64, prime(8)=19, 6+4=1+9
11^2=121, prime(11)=31, 1+2+1=3+1
22^2=484, prime(22)=79, 4+8+4=7+9
34^2=1156, prime(22)=139, 1+1+5+6=1+3+9.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A117224 Numbers for which the square and the cube have the same digital sum, A007605 Sum of digits of n-th prime, A004159 Sum of digits of n^2.

Programs

Mathematica

Position[Table[Plus@@IntegerDigits[Prime[n]]-Plus@@IntegerDigits[n^2],{n,1,3000}],0]//Flatten
Select[Range[2000],Total[IntegerDigits[#^2]]==Total[IntegerDigits[ Prime[ #]]]&] (* Harvey P. Dale, May 22 2015 *)