A028822 Squares with digits in nonincreasing order.

0, 1, 4, 9, 64, 81, 100, 400, 441, 841, 900, 961, 6400, 7744, 8100, 10000, 40000, 44100, 84100, 90000, 96100, 640000, 774400, 810000, 1000000, 4000000, 4410000, 8410000, 8874441, 9000000, 9610000, 9853321, 64000000, 77440000

Offset

1,3

Comments

From Robert G. Wilson v, Jan 02 2014: (Start)

If x is present so is 100x. The primitives are 0, 1, 4, 9, 64, 81, 441, 841, 961, 7744, 8874441, 9853321, 999887641, …, . = A062826. Their square roots are: 0, 1, 2, 3, 8, 9, 21, 29, 31, 88, 2979, 3139, 31621, …, . Are there no more primitives?

Number of terms less than 10^k, beginning with k=0: 1, 4, 6, 12, 15, 21, 24, 32, 35, 44, 47, 56, 59, 68, 71, 80, 83, 92, 95, …, .

Like all squares the ending digits can be 0, 1, 4, 5, 6 or 9. Here is the tally of the list of terms < 10^18: {0, 84}, {1, 8}, {4, 3}, {5, 0}, {6, 0}, {9, 1}. (End)

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..96

P. De Geest, Palindromic Squares

Formula

For n > 1, a(n) = A062826(i) * 10^j for some i and j. - Charles R Greathouse IV, Jan 02 2014

a(n) = A028821(n)^2. - Ray Chandler, Jan 05 2014

Mathematica

fQ[n_] := Max[ Differences[ IntegerDigits[ n]]] < 1; Select[ Range[0, 9000]^2, fQ] (* Robert G. Wilson v, Jan 02 2014 *)
Select[Range[0, 10^4]^2, GreaterEqual@@IntegerDigits[#]&] (* Ray Chandler, Jan 05 2014 *)

Prog

(PARI) isA009996(n)=n=digits(n); for(i=2, #n, if(n[i]>n[i-1], return(0))); 1
is(n)=issquare(n) && isA009996(n) \\ Charles R Greathouse IV, Jan 02 2014

Crossrefs

Cf. A062826, A028820, A028821, A009996.

Sequence in context: A062758 A217854 A369866 * A270696 A069495 A029788

Adjacent sequences: A028819 A028820 A028821 * A028823 A028824 A028825

Keyword

nonn,base

Author

Patrick De Geest

Extensions

Better name from Robert G. Wilson v, Jan 02 2014

Status

approved