A321513 Numbers that are periodic in base 4, written in decimal, where the base-4 expansion contains at least two periods.

5, 10, 15, 17, 21, 34, 42, 51, 63, 65, 68, 85, 102, 119, 130, 136, 153, 170, 187, 195, 204, 221, 238, 255, 257, 260, 273, 325, 341, 390, 455, 514, 520, 546, 585, 650, 682, 715, 771, 780, 819, 845, 910, 975, 1023, 1025, 1028, 1040, 1092, 1105, 1170, 1235, 1285

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Example

The base-4 representation of 17 is 101, which is periodic when considering leading zeros, i.e., 0101, so 17 is a term of the sequence.
The base-4 representation of 170 is 2222, which is periodic, so 170 is a term of the sequence.
The base-4 representation of 1495 is 113113, which is periodic, so 1495 is a term of the sequence.

Prog

(PARI) subvec(vec, pos, len) = my(w=[]); for(k=pos, pos+len-1, if(k > #vec, return(0), w=concat(w, vec[k]))); w
is_perio(vec) = my(d=divisors(#vec), v=[], w=[]); for(x=2, #d-1, v=subvec(vec, 1, d[x]); forstep(y=1, #vec, d[x], w=subvec(vec, y, d[x]); if(w!=v, break, if(y+d[x] >= #vec, return(1))))); 0
is(n) = my(d=digits(n, 4), z=[]); if(#d < 2, return(0)); if(vecmin(d)==vecmax(d), return(1)); while(#z <= #d, if(is_perio(concat(z, d)), return(1)); z=concat(z, [0])); 0
(PARI) is(n, b=4) = for (w=1, oo, my (d=digits(n, b^w)); if (#d<=1, return (0), #Set(d)==1, return (1))) \\ Rémy Sigrist, Nov 16 2018

Crossrefs

Cf. A007090, A242139.

Sequence in context: A353167 A254063 A313670 * A188043 A313671 A313672

Adjacent sequences: A321510 A321511 A321512 * A321514 A321515 A321516

Keyword

nonn,base

Author

Felix Fröhlich, Nov 11 2018

Status

approved