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A247047 Numbers n such that n^2 contains 2 distinct digits and n^3 contains 3 distinct digits. 0
5, 6, 8, 9, 15, 30, 173, 300, 3000, 30000, 300000, 3000000, 30000000, 300000000, 3000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A016069 and A155146.

This sequence is infinite since 3*10^n is always in this sequence for n > 0.

Is 173 the last term not of the form 3*10^n?

3*10^7 < a(14) <= 3*10^8.

The numbers n such that n^2 contains 2 distinct digits, n^3 contains 3 distinct digits, and n^4 contains 4 distinct digits are conjectured to only be 6, 8, and 15. (Intersection of A016069, A155146, and A155150.)

LINKS

Table of n, a(n) for n=1..15.

PROG

(PARI)

for(n=1, 3*10^7, d2=digits(n^2); d3=digits(n^3); if(#vecsort(d2, , 8)==2&&#vecsort(d3, , 8)==3, print1(n, ", ")))

(Python)

A247047_list = [n for n in range(1, 10**6) if len(set(str(n**3))) == 3 and len(set(str(n**2))) == 2]

# Chai Wah Wu, Sep 26 2014

CROSSREFS

Cf. A016069, A155146.

Sequence in context: A308708 A125251 A271728 * A218866 A227760 A055592

Adjacent sequences:  A247044 A247045 A247046 * A247048 A247049 A247050

KEYWORD

nonn,base,more

AUTHOR

Derek Orr, Sep 10 2014

EXTENSIONS

a(14)-a(15) from Chai Wah Wu, Sep 26 2014

STATUS

approved

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Last modified September 21 09:06 EDT 2021. Contains 347597 sequences. (Running on oeis4.)