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 A306520 Numbers k with property that the arithmetic mean of any subset of its digits is an integer. 1
 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 2-digit 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 Harvey P. Dale, Table of n, a(n) for n = 1..177 (* All terms up to 1 million *) 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. MATHEMATICA Select[Range[0, 200], AllTrue[Mean/@Subsets[IntegerDigits[#], {2, IntegerLength[ #]}], IntegerQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 09 2020 *) 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:  A306517 A306518 A306519 * A306521 A306522 A306523 KEYWORD nonn,base AUTHOR R. J. Cano, Feb 21 2019 STATUS approved

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Last modified June 25 03:09 EDT 2021. Contains 345449 sequences. (Running on oeis4.)