A197039 -id:A197039 - cp's OEIS frontend

A225534 Numbers whose sum of cubed digits is prime.

11, 101, 110, 111, 113, 115, 122, 124, 128, 131, 139, 142, 146, 148, 151, 155, 164, 166, 182, 184, 193, 199, 212, 214, 218, 221, 223, 227, 232, 236, 238, 241, 245, 254, 256, 263, 265, 269, 272, 278, 281, 283, 287, 289, 296, 298, 311, 319, 322, 326, 328, 335

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, May 10 2013

Note that 11 is the only two-digit number in the sequence.

a(n) ~ n. For 414 < n < 10000, 6.38*n - 528 provides an estimate of a(n) to within 6%.

			139 is in the sequence because 1^3 + 3^3 + 9^3 = 757, which is prime.

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

Cf. A197039, A055012, A046459, A225535.
Cf. A165330, A046197.
Cf. A046704, A023194.

Select[Range[350],PrimeQ[Total[IntegerDigits[#]^3]]&] (* Harvey P. Dale, Mar 16 2016 *)

digcubesum<-function(x) sum(as.numeric(strsplit(as.character(x),split="")[[1]])^3); library(gmp);
which(sapply(1:1000,function(x) isprime(digcubesum(x))>0))

A225535 Numbers whose cubed digits sum to a cube, and have more than one nonzero digit.

Original entry on oeis.org

168, 186, 345, 354, 435, 453, 534, 543, 618, 681, 816, 861, 1068, 1086, 1156, 1165, 1516, 1561, 1608, 1615, 1651, 1680, 1806, 1860, 3045, 3054, 3405, 3450, 3504, 3540, 4035, 4053, 4305, 4350, 4503, 4530, 5034, 5043, 5116, 5161, 5304, 5340, 5403, 5430, 5611

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, May 10 2013

			5^3 + 6^3 + 1^3 + 1^3 = 343, which is 7^3.

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

Cf. A225534 (cubed digits sum to a prime), A197039 (square), A046459. A055012.
Cf. A165330 (cube cycle), A046197 (cubic fixed points), A000578 (cubes).
Cf. A052034 (squared digits sum to a prime), A028839, A117685.
Cf. A164882 (n such that sum of the cubes of the digits of n^3 is perfect cube). - Zak Seidov, May 21 2013

fQ[n_] := Module[{d = IntegerDigits[n]}, Count[d, 0] + 1 < Length[d] && IntegerQ[Total[d^3]^(1/3)]]; Select[Range[5611], fQ] (* T. D. Noe, May 19 2013 *)

y=rep(0,10000); len=0; x=0; library(gmp);
digcubesum<-function(x) sum(as.numeric(unlist(strsplit(as.character(as.bigz(x)),split="")))^3);
iscube<-function(x) ifelse(as.bigz(x)<2,T,all(table(as.numeric(factorize(x)))%%3==0));
nonzerodig<-function(x) sum(strsplit(as.character(x),split="")[[1]]!="0");
which(sapply(1:6000,function(x) nonzerodig(x)>1 & iscube(digcubesum(x))))

A197129 Numbers such that the sum, sum of the squares, and sum of the cubes of the decimal digits are each a perfect square.

Original entry on oeis.org

1, 4, 9, 10, 40, 90, 100, 400, 900, 1000, 1111, 1224, 1242, 1339, 1393, 1422, 1933, 2124, 2142, 2214, 2241, 2412, 2421, 3139, 3193, 3319, 3391, 3913, 3931, 4000, 4122, 4212, 4221, 4444, 4669, 4696, 4966, 6469, 6496, 6649, 6694, 6946, 6964, 9000, 9133, 9313

Offset: 1

Michel Lagneau, Oct 10 2011

Each number > 90 contains at least two identical digits because the sequence A197125 contains a subset of numbers all of whose digits are distinct and are all the permutations of 1567890. But 1^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 = 1926 is not square. Consequently, it is impossible to find numbers > 90 with distinct digits in this sequence.

			4669 is in the sequence because:
4   + 6   + 6   + 9   = 25   = 5^2;
4^2 + 6^2 + 6^2 + 9^2 = 169  = 13^2;
4^3 + 6^3 + 6^3 + 9^3 = 1225 = 35^2.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A028839, A175396, A197039, A197125.

for n from 1 to 10000 do:l:=evalf(floor(ilog10(n))+1):n0:=n:s1:=0:s2:=0:s3:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10): n0:=v :s1:=s1+u:s2:=s2+u^2:s3:=s3+u^3:od:if sqrt(s1)=floor(sqrt(s1)) and sqrt(s2)=floor(sqrt(s2)) and sqrt(s3)=floor(sqrt(s3))then printf(`%d, `, n): else fi:od:

sdQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[Sqrt[Total[idn^2]]]&&IntegerQ[Sqrt[Total[idn^3]]]]; Select[ Range[ 10000],sdQ] (* Harvey P. Dale, Oct 25 2011 *)
psQ[n_]:=With[{idn=IntegerDigits[n]},AllTrue[{Sqrt[Total[idn]],Sqrt[Total[idn^2]],Sqrt[Total[idn^3]]},IntegerQ]]; Select[Range[10000],psQ] (* Harvey P. Dale, Nov 17 2024 *)

is(n)=my(v=eval(Vec(Str(n))));issquare(sum(i=1,#v,v[i]))&&issquare(sum(i=1,#v,v[i]^2))&&issquare(sum(i=1,#v,v[i]^3)) \\ Charles R Greathouse IV, Oct 10 2011

A028839 INTERSECT A175396 INTERSECT A197039.

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A225534 Numbers whose sum of cubed digits is prime.

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A225535 Numbers whose cubed digits sum to a cube, and have more than one nonzero digit.

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A197129 Numbers such that the sum, sum of the squares, and sum of the cubes of the decimal digits are each a perfect square.

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