OFFSET
1,2
COMMENTS
There are 117 such n's < 10^7: 1, 1049, 1490, 10002, 10005, 10011, 10020, 10050, 10101, 10110, 10149, 10200, 10500, 11001, 11010, 11100, 11490, 12000, 14499, 15000, 17610, 18000, 20001, 20010, 20100, 21000, 24900, 30000, 33200, 35000, 36100, 44900, 44990, 45100, 46000, 54800, 55000, 64900, 71000, 80000, 1000006, 1000015, 1000051, 1000055, 1000060, 1000105, 1000150, 1000501, 1000510, 1000550, 1000600, 1001005, 1001050, 1001500, 1005001, 1005010, 1005100, 1005500, 1006000, 1006490, 1009951, 1010005, 1010050, 1010149, 1010500, 1011490, 1015000, 1024900, 1050001, 1050010, 1050100, 1051000, 1055000, 1060000, 1064900, 1095500, 1096000, 1100005, 1100050, 1100500, 1105000, 1114900, 1145000, 1150000, 1190000, 1224749, 1244990, 1249000, 1414249, 1415000, 1420000, 1424900, 1429000, 1451000, 1460000, 1484251, 1500001, 1500010, 1500100, 1501000, 1510000, 1550000, 1600000, 1735000, 1739000, 1789000, 1820000, 2000005, 2000050, 2000500, 2005000, 2050000, 2239000, 2261000, 2450000, 2500000, 2900000.
Or: Numbers k such that k^2 is in A061384, i.e., square root of squares in A061384. - M. F. Hasler, Dec 05 2010
FORMULA
EXAMPLE
1049 is a term because 1049^2 = 1100401 and (1 + 1 + 0 + 0 + 4 + 0 + 1)/7 = 1.
MATHEMATICA
Select[Range[50000], Mean[IntegerDigits[#^2]]==1&] (* Harvey P. Dale, Dec 15 2014 *)
PROG
(PARI) {for(d=1, 9, for(n=sqrtint(10^(d-1)-1)+1, sqrtint(10^d-1), my(n2=divrem(n^2, 10)); sum( k=2, d, (n2=divrem(n2[1], 10))[2], n2[2])/d==1 & print1(n", ")))} \\ M. F. Hasler, Dec 05 2010
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Zak Seidov, Aug 26 2009
EXTENSIONS
Terms up to a(117) checked with given PARI code by M. F. Hasler, Dec 05 2010
STATUS
approved