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A368408
a(n) is the least start of a run of exactly n consecutive integers with an even number of Fermi-Dirac factors (A064547).
1
1, 14, 20, 62, 32, 115, 1464, 141, 1343, 3090, 1135, 13382, 47752, 126658, 246406, 68420, 1277700, 205737, 4457044, 382196, 2211385, 21274837, 9444464, 29186922, 52699949, 140918773, 185359148, 108907632, 218549045, 2655616337, 7466369825, 2879711373, 20145833217, 34980297750, 42278164437
OFFSET
1,2
MATHEMATICA
q[n_] := EvenQ[Sum[DigitCount[e, 2, 1], {e, FactorInteger[n][[;; , 2]]}]]; q[1] = True; seq[len_] := Module[{s = Table[0, {len}], n = 1, count = 0, n1, d}, While[count < len, n1 = n; If[q[n], While[q[++n1]]; d = n1 - n; If[d <= len && s[[d]] == 0, count++; s[[d]] = n]]; n = n1 + 1]; s]; seq[16]
PROG
(PARI) is(n) = {my(e = factor(n)[, 2]); !(sum(i = 1, #e, hammingweight(e[i])) % 2); }
lista(len) = {my(s = vector(len), n = 1, count = 0, n1, d); while(count < len, n1 = n; if(is(n), n1++; while(is(n1), n1++); d = n1 - n; if(d <= len && s[d] == 0, count++; s[d] = n)); n = n1 + 1); s};
CROSSREFS
Analogous to A275508.
Sequence in context: A067796 A015797 A293184 * A064974 A167335 A129244
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 23 2023
STATUS
approved