A032743 Super-2 Numbers (2 * n^2 contains substring '22' in its decimal expansion).

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

Offset

1,1

Comments

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

Conjecture: a(n) ~ n. - Charles R Greathouse IV, Dec 04 2024

References

C. A. Pickover, "Keys to Infinity", New York: Wiley, p. 7, 1995.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Giovanni Resta, super-d numbers, personal web site "Numbers Aplenty", 2013

Eric Weisstein's World of Mathematics, Super-d Number.

Mathematica

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 *)

Prog

(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
(Python) is_A032743=lambda n, d=2: str(d)*d in str(d*n**d) # M. F. Hasler, Jul 16 2024

Crossrefs

Cf. A014569 (similar for d=3), A032744 - A032749 (similar for d=4, ..., 9).

Sequence in context: A033212 A104227 A274507 * A106861 A107168 A243450

Adjacent sequences: A032740 A032741 A032742 * A032744 A032745 A032746

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Status

approved