A209303 -id:A209303 - cp's OEIS frontend

A307735 Integers k such that if m = k + A003132(k) then k = m - A003132(m).

0, 9, 205, 212, 217, 366, 457, 663, 1314, 1315, 1348, 1672, 1742, 1792, 1797, 2005, 2012, 2017, 2129, 2201, 2208, 2213, 2216, 2305, 2404, 2405, 2465, 2564, 2565, 2671, 2741, 2748, 2789, 2829, 3114, 3115, 3205, 3303, 3306, 3394, 3436, 3475, 3696, 3819, 4204, 4205, 4245, 4347, 4475, 4542, 4629, 4647, 4688

Offset: 1

Antonio Roldán, Apr 25 2019

A003132(n) is the sum of the squares of the digits of n.

			205 is in the sequence because 205 + 2^2 + 0^2 + 5^2 = 234 and 234 - 2^2 - 3^2 - 4^2 = 205.

Cf. A003132, A108662, A175396, A209303, A223035, A225049, A258881.

sod2[n_] := Total @ (IntegerDigits[n]^2); aQ[n_] := sod2[n + (s=sod2[n])] == s; Select[Range[0, 4700], aQ] (* Amiram Eldar, Jul 03 2019 *)

for(i = 0 , 5000 , a = i + norml2(digits(i)) ; b = a - norml2(digits(a)) ; if(i == b , print1(i , ", ")))

A225065 Numbers of the form n^2 plus the sum of squared digits of n^2.

Original entry on oeis.org

2, 20, 53, 54, 81, 90, 101, 116, 127, 146, 177, 258, 287, 314, 321, 353, 407, 416, 438, 474, 580, 639, 686, 690, 797, 863, 913, 922, 981, 1045, 1079, 1219, 1235, 1259, 1418, 1493, 1496, 1552, 1637, 1783, 1866, 2011, 2058, 2063, 2158, 2298, 2333, 2422, 2529

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, Apr 26 2013

Note that consecutive terms are not necessarily generated by consecutive values of n.

It appears that 146 is the only term that can be generated by two values of n (7 and 9). There are no other duplicates in the first 10000 terms.

			For n=11: 11^2=121; 121 + 1^2 + 2^2 + 1^2 = 127.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Cf. A176995, A062028, A209303.

sort(unique((1:101)^2+sapply((1:101)^2,function(x) sum(as.numeric(unlist(strsplit(as.character(x),split="")))^2))))

A225051 Numbers of the form x^3 + SumOfCubedDigits(x).

Original entry on oeis.org

0, 2, 16, 54, 128, 250, 432, 686, 1024, 1458, 1001, 1333, 1737, 2225, 2809, 3501, 4313, 5257, 6345, 7589, 8008, 9270, 10664, 12202, 13896, 15758, 17800, 20034, 22472, 25126, 27027, 29819, 32803, 35991, 39395, 43027, 46899, 51023, 55411, 60075, 64064, 68986

Offset: 0

Jonathan Vos Post, Apr 25 2013

This is to cubes A000578 as A209303 is to squares A000290.

			a(1) = 1^3 + 1^3 = 2; a(10) = 10^3 + (1^3 + 0^3) = 1000 + 1.

Cf. A000578, A055012, A209303.

Table[n^3 + Total[IntegerDigits[n]^3], {n, 0, 50}] (* T. D. Noe, Apr 26 2013 *)

a(n) = A000578(n) + A055012(n).

cp's OEIS Frontend

A307735 Integers k such that if m = k + A003132(k) then k = m - A003132(m).

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A225065 Numbers of the form n^2 plus the sum of squared digits of n^2.

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A225051 Numbers of the form x^3 + SumOfCubedDigits(x).

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