A028845 -id:A028845 - cp's OEIS frontend

A050626 Product of digits of n is a nonzero square.

1, 4, 9, 11, 14, 19, 22, 28, 33, 41, 44, 49, 55, 66, 77, 82, 88, 91, 94, 99, 111, 114, 119, 122, 128, 133, 141, 144, 149, 155, 166, 177, 182, 188, 191, 194, 199, 212, 218, 221, 224, 229, 236, 242, 248, 263, 281, 284, 289, 292, 298, 313, 326, 331, 334, 339, 343

Offset: 1

Patrick De Geest, Jun 15 1999

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

Cf. A007954, A028845, A028839.

[ n: n in [1..350] | s gt 0 and IsSquare(s) where s is &*Intseq(n,10) ];  // Bruno Berselli, May 26 2011

Select[Range[500],DigitCount[#,10,0]==0&&IntegerQ[Sqrt[Times@@ IntegerDigits[ #]]]&] (* Harvey P. Dale, Jun 09 2020 *)

is(n)=my(v=digits(n),pr=prod(i=1,#v,v[i]));pr&&issquare(pr) \\ Charles R Greathouse IV, May 19 2013

A028837 Iterated sum of digits of n is a square.

Original entry on oeis.org

1, 4, 9, 10, 13, 18, 19, 22, 27, 28, 31, 36, 37, 40, 45, 46, 49, 54, 55, 58, 63, 64, 67, 72, 73, 76, 81, 82, 85, 90, 91, 94, 99, 100, 103, 108, 109, 112, 117, 118, 121, 126, 127, 130, 135, 136, 139, 144, 145, 148, 153, 154, 157, 162, 163, 166, 171, 172, 175, 180

Offset: 1

N. J. A. Sloane

			E.g. 58 -> 5+8 = 13 -> 1+3 = 4 is a square.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A010888, A028839, A028845.

LinearRecurrence[{1,0,1,-1},{1,4,9,10},60] (* Harvey P. Dale, Jan 26 2015 *)

a(n) = a(n-3)+9. If n is a multiple of 3 then a(n) = 3n, otherwise a(n) = 3n-2. Numbers of form {0, 1, 4} modulo 9 - Henry Bottomley, Jun 30 2000
a(1)=1, a(2)=4, a(3)=9, a(4)=10, a(n)=a(n-1)+a(n-3)-a(n-4). - Harvey P. Dale, Jan 26 2015
G.f.: x*(1+3*x+5*x^2) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Sep 22 2016
E.g.f.: (exp(x)*(9*x - 4) + 4*exp(-x/2)*cos(sqrt(3)*x/2))/3. - Stefano Spezia, Mar 07 2024

More terms from Patrick De Geest, Jun 15 1999

A050627 Product of digits of n is a nonzero single-digit square.

Original entry on oeis.org

1, 4, 9, 11, 14, 19, 22, 33, 41, 91, 111, 114, 119, 122, 133, 141, 191, 212, 221, 313, 331, 411, 911, 1111, 1114, 1119, 1122, 1133, 1141, 1191, 1212, 1221, 1313, 1331, 1411, 1911, 2112, 2121, 2211, 3113, 3131, 3311, 4111, 9111, 11111, 11114, 11119, 11122, 11133

Offset: 1

Patrick De Geest, Jun 15 1999

I.e., the product of digits is 1, 4, or 9. - Franklin T. Adams-Watters, Sep 27 2016

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007954, A028845, A028839, A002275 (a subsequence).

f:= proc(d) local R,i;
  R:= [1$d],seq([1$i,4,1$(d-1-i)],i=0..d-1),seq([1$i,9,1$(d-1-i)],i=0..d-1);
  if d >= 2 then R:= R, op(combinat:-permute([1$(d-2),2,2])), op(combinat:-permute([1$(d-2),3,3])) fi;
  op(sort(map(proc(L) local i; add(L[i]*10^(i-1),i=1..d) end proc, [R])))
end proc:
map(f, [$1..6]); # Robert Israel, Apr 09 2025

Select[Range[12000],MemberQ[{1,4,9},Times@@IntegerDigits[#]]&] (* Harvey P. Dale, Jan 22 2016 *)

cp's OEIS Frontend

A050626 Product of digits of n is a nonzero square.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A028837 Iterated sum of digits of n is a square.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A050627 Product of digits of n is a nonzero single-digit square.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica