

A306520


Numbers k with property that the arithmetic mean of any subset of its digits is an integer.


0



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 111, 117, 135, 153, 159, 171, 177, 195
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

This sequence is different from A061383. Here digits in k must have all the same parity, otherwise the average of at least a pair of digits wouldn't be an integer. Note that for every 2digit term in A061383 both digits have the same parity. But not every number whose digits have all the same parity (sequence A059708) belongs here.


LINKS

Table of n, a(n) for n=1..63.


FORMULA

Apparently a(158+n) = A010785(35+n).


EXAMPLE

17 is in this sequence because the set of digits (1,7) has an integer average: 4.
159 and 195 are in this sequence because the sets of digits (1,5), (1,9), (5,9), and (1,5,9) all have integer averages, respectively: 3, 5, 7, and 5.


PROG

(PARI) firstTerms_vec(n)={my(v=vector(n), c, t, w:list, h); for(i=1, +oo, w=List(); forsubset(i, k, listput(w, k)); listpop(w, 1); forvec(j=vector(i, z, [(z==1)&&(i>1), 9]), h=j[1]%2; for(l=2, #j, if((j[l]%2)!=h, next(2))); for(k=1, #w, t=vecextract(j, w[k]); if(vecsum(t)%(#w[k]), next(2))); v[c++]=fromdigits(j); if(c==n, return(v))))}
(PARI) isok(m, {B=10})={my(w=digits(m, B)); forsubset(#w, y, if(y!=Vecsmall([]), if(vecsum(vecextract(w, y))%(#y), return(0)), next)); 1}


CROSSREFS

Cf. A061383, A059708, A010785, A165165.
Sequence in context: A275945 A061383 A059708 * A247945 A317621 A298297
Adjacent sequences: A306513 A306518 A306519 * A306522 A306523 A306524


KEYWORD

nonn,base


AUTHOR

R. J. Cano, Feb 21 2019


STATUS

approved



