A331898 -id:A331898 - cp's OEIS frontend

A337842 The smallest palindrome with exactly n circular loops (or holes) in its decimal representation.

1, 0, 8, 606, 88, 808, 888, 68086, 8888, 88088, 88888, 6880886, 888888, 8880888, 8888888, 688808886, 88888888, 888808888, 888888888, 68888088886, 8888888888, 88888088888, 88888888888, 6888880888886, 888888888888, 8888880888888, 8888888888888, 688888808888886

Offset: 0

Bernard Schott, Sep 25 2020

The decimal digits 1, 2, 3, 5, 7 have no hole, and 4 is represented without a hole; otherwise, 0, 6, 9 have one hole each and 8 has two holes.
Least palindrome q such that A064532(q) = n.
Except for a(0) = 1, each term has only digits 0, 6 or 8 in its decimal expansion.

			a(3) = 606 because 6 and 0 have each one circular loop for a total of 3.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for sequences related to holes in digits
Index entries for linear recurrences with constant coefficients, signature (0,0,0,111,0,0,0,-1110,0,0,0,1000).

Cf. A000533, A002113, A002282, A064532, A332180.

Cf. A331898 (similar for primes).

a[0] = 1; a[n_] := Switch[Mod[n, 4], ?EvenQ, 8*(10^(n/2) - 1)/9, 1, 8*(10^((n + 1)/2) - 9*10^((n - 1)/4) - 1)/9, 3, 8*(10^((n + 3)/2) - 9*10^((n + 1)/4) - 1)/9 - 2*(10^((n + 1)/2) + 1)]; Array[a, 28, 0] (* _Amiram Eldar, Sep 26 2020 *)
LinearRecurrence[{0,0,0,111,0,0,0,-1110,0,0,0,1000},{1,0,8,606,88,808,888,68086,8888,88088,88888,6880886,888888},30] (* Harvey P. Dale, Mar 13 2022 *)

a(2m) = A002282(m) for m >= 1.
a(4m+1) = A332180(m) for m >= 1.
a(4m+3) = 6 * A000533(2m+2) + 10 * A332180(m) for m >= 0.

More terms from Amiram Eldar, Sep 25 2020

A359245 The smallest square with exactly n circular loops (or holes) in its decimal expansion (A064532).

Original entry on oeis.org

1, 0, 81, 289, 1089, 8836, 6889, 80089, 688900, 1868689, 8508889, 29888089, 288898009, 983888689, 3808988089, 8680089889, 86908808809, 488088068689, 878686888689, 2888986888804, 48890888808804, 108506888888896, 88869893888889, 880881089888881, 788088668888889

Offset: 0

Bernard Schott, Dec 22 2022

The digit 8 has two loops, the digits 0, 6 and 9 have one loop, and other digits (including 4) have no hole.

Least square k such that A064532(k) = n.

			a(3) = 289 because 8 has two loops and 9 has one loop for a total of 3, and 289 is the smallest such square.

Cf. A064532.

Similar: A331898 (primes), A337842 (palindromes).

a(n) = { for (k=0, oo, my (d=digits(k^2)); if (n==(k==0)+sum(i=1, #d, [1, 0, 0, 0, 0, 0, 1, 0, 2, 1][1+d[i]]), return (k^2))) } \\ Rémy Sigrist, Dec 22 2022

More terms from Rémy Sigrist, Dec 22 2022

cp's OEIS Frontend

A337842 The smallest palindrome with exactly n circular loops (or holes) in its decimal representation.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions