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A321513
Numbers that are periodic in base 4, written in decimal, where the base-4 expansion contains at least two periods.
3
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
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
Sequence in context: A353167 A254063 A313670 * A188043 A313671 A313672
KEYWORD
nonn,base
AUTHOR
Felix Fröhlich, Nov 11 2018
STATUS
approved