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A326418 Nonnegative numbers k such that, in decimal representation, the subsequence of digits of k^2 occupying an odd position is equal to the digits of k. 1
0, 1, 5, 6, 10, 11, 50, 60, 76, 100, 105, 110, 500, 501, 505, 506, 600, 605, 756, 760, 826, 1000, 1001, 1050, 1100, 5000, 5010, 5050, 5060, 5941, 6000, 6050, 7560, 7600, 8260, 10000, 10005, 10010, 10500, 10505, 11000, 12731 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If k is in the sequence then so is 10*k. - David A. Corneth, Sep 29 2019

LINKS

David A. Corneth, Table of n, a(n) for n = 1..2361 (first 485 terms from Charles R Greathouse IV, terms < 10^15)

EXAMPLE

5^2 = 25, whose first digit is 5, hence 5 is a term of the sequence.

11^2 = 121, whose first and third digit are (1, 1), hence 11 is a term of the sequence.

756^2 = 571536, whose digits in odd positions - starting from the least significant one - are (7, 5, 6), hence 756 is a term of the sequence.

MATHEMATICA

Select[Range[0, 13000], Reverse@ #[[-Range[1, Length@ #, 2]]] &@ IntegerDigits[#^2] === IntegerDigits[#] &] (* Michael De Vlieger, Oct 06 2019 *)

PROG

(PARI) isok(n) = my(d=Vecrev(digits(n^2))); fromdigits(Vecrev(vector((#d+1)\2, k, d[2*k-1]))) == n; \\ Michel Marcus, Oct 01 2019

(Python)

def ok(n): s = str(n*n); return n == int("".join(s[1-len(s)%2::2]))

print(list(filter(ok, range(13000)))) # Michael S. Branicky, Sep 10 2021

CROSSREFS

Subsequence of A008851, A029772, A046829, A064827, A052212, and A189056.

Sequence in context: A046829 A052212 A046838 * A037359 A099538 A093614

Adjacent sequences:  A326415 A326416 A326417 * A326419 A326420 A326421

KEYWORD

nonn,base

AUTHOR

Riccardo Pietro Giovambattista Mazzei and Matteo Albanese, Sep 28 2019

STATUS

approved

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Last modified September 25 20:01 EDT 2021. Contains 347659 sequences. (Running on oeis4.)