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A032743
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Super-2 Numbers (2 * n^2 contains substring '22' in its decimal expansion).
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9
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19, 31, 69, 81, 105, 106, 107, 119, 127, 131, 169, 181, 190, 219, 231, 247, 269, 281, 310, 318, 319, 331, 332, 333, 334, 335, 336, 337, 338, 339, 348, 369, 381, 419, 431, 454, 469, 481, 511, 519, 531, 558, 569, 581, 601, 619, 631, 669, 679, 681, 690, 715
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OFFSET
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1,1
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COMMENTS
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For any term a(n), all numbers a(n)*10^k, k >= 0, are also in the sequence. Moreover, the first four terms satisfy 2*a(n)^2 == 22 (mod 100), therefore any number ending in 19, 31, 69 or 81 (possibly followed by trailing '0's) is in the sequence. - M. F. Hasler, Jul 16 2024
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REFERENCES
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C. A. Pickover, "Keys to Infinity", New York: Wiley, p. 7, 1995.
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LINKS
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MATHEMATICA
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Select[Range[1000], MemberQ[Partition[IntegerDigits[2#^2], 2, 1], {2, 2}]&] (* Harvey P. Dale, May 09 2012 *)
Select[Range[750], SequenceCount[IntegerDigits[2#^2], {2, 2}]>0&] (* Harvey P. Dale, May 13 2022 *)
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PROG
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(PARI) select( {is_A032743(n, d=2, m=10^d, r=m\9*d)=n=d*n^d; until(r>n\=10, n%m==r && return(1))}, [0..999]) \\ M. F. Hasler, Jul 16 2024
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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