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A028822 Squares with digits in nonincreasing order. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A168251 A062758 A217854 * 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

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Last modified August 21 06:02 EDT 2019. Contains 326162 sequences. (Running on oeis4.)