A254066 Primitive numbers n such that the sums of the digits of n and n^2 coincide.

1, 9, 18, 19, 45, 46, 55, 99, 145, 189, 198, 199, 289, 351, 361, 369, 379, 388, 451, 459, 468, 495, 496, 558, 559, 568, 585, 595, 639, 729, 739, 775, 838, 855, 954, 955, 999, 1098, 1099, 1179, 1188, 1189, 1198, 1269, 1468, 1485, 1494, 1495, 1585, 1738, 1747

Offset: 1

Author

Nikhil Mahajan, Jan 25 2015

Keywords

• nonn
• base

Comments

Members of A058369 not congruent to 0 (mod 10).

This sequence is to A058369 what A114135 is to A111434.

Hare, Laishram, & Stoll show that this sequence is infinite. In particular for each k in {846, 847, 855, 856, 864, 865, 873, ...} there are infinitely many terms in this sequence with digit sum k. - Charles R Greathouse IV, Aug 25 2015

Examples

			9 is in the sequence because the digit sum of 9^2 = 81 is 9.
18 is in the sequence because the digit sum of 18^2 = 324 is 9, same as the digit sum of 18.
		

Links

• Nikhil Mahajan, Table of n, a(n) for n = 1..10000
• K. G. Hare, S. Laishram, and T. Stoll, The sum of digits of n and n^2, International Journal of Number Theory 7:7 (2011), pp. 1737-1752.

Crossrefs

Cf. A058369, A114135, A111434.

Subsequence of A090570.

Programs

Magma

[n: n in [1..1000] | &+Intseq(n) eq &+Intseq(n^2) and not IsZero(n mod 10)]; // Bruno Berselli, Jan 29 2015

Mathematica

Select[Range[1000],!Divisible[#,10]&&Total[IntegerDigits[#]] == Total[ IntegerDigits[#^2]]&] (* Harvey P. Dale, Dec 27 2015 *)

PARI

is(n)=sumdigits(n)==sumdigits(n^2) \\ Charles R Greathouse IV, Aug 25 2015

PARI

list(lim)=my(v=List()); forstep(n=1,lim,[8, 9, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 8, 1, 9], if(sumdigits(n)==sumdigits(n^2), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Aug 26 2015

Sage

[n for n in [0..1000] if sum(n.digits())==sum((n^2).digits()) and n%10!=0] # Tom Edgar, Jan 27 2015

Extensions

More terms from Harvey P. Dale, Dec 27 2015