A369235 - OEIS

A369235

The 180-degree rotations of those numbers which can be rotated 180 degrees, where digits 2 and 7 are 180-degree rotations of each other.

0, 1, 7, 9, 2, 8, 6, 1, 11, 71, 91, 21, 81, 61, 7, 17, 77, 97, 27, 87, 67, 9, 19, 79, 99, 29, 89, 69, 2, 12, 72, 92, 22, 82, 62, 8, 18, 78, 98, 28, 88, 68, 6, 16, 76, 96, 26, 86, 66, 1, 101, 701, 901, 201, 801, 601, 11, 111, 711, 911, 211, 811, 611, 71, 171, 771, 971, 271, 871, 671

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Numbers which can be rotated are those having only decimal digits 0, 1, 2, 6, 7, 8, 9 (none of 3, 4, 5).

180-degree rotation is digit reversal and mapping 2 <-> 7 and 6 <-> 9 (and leading 0s are discarded from the result).

Digits 2 and 7 are taken to be 180-degree rotations of each other, though visually this may require a font designed to facilitate ambigrams.

LINKS

Table of n, a(n) for n=0..69.

MATHEMATICA

lst = {}; fQ[n_] := Block[{s = {0, 1, 2, 6, 7, 8, 9}, id = IntegerDigits[n]}, If[ Union[ Join[s, id ]] == s, AppendTo[lst, FromDigits[Reverse[(id /. {2 -> 7, 7 -> 2, 6 -> 9, 9 -> 6})]]], False]]; Select[ Range[0, 1000], fQ[#] &]; lst

PROG

(PARI) my(flip=[0, 1, 7, 9, 2, 8, 6]); \

a(n) = fromdigits([flip[d+1] |d<-Vecrev(digits(n, 7))]); \\ Kevin Ryde, Jan 18 2024

CROSSREFS

Sequence in context: A316246 A249546 A336076 * A110793 A199290 A309644

Adjacent sequences: A369232 A369233 A369234 * A369236 A369237 A369238

KEYWORD

nonn,base,easy

AUTHOR

Darrell W. Acree, Jan 17 2024

STATUS

approved