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, 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

Author

Amiram Eldar, Dec 23 2023

Keywords

• nonn
• base

Crossrefs

Cf. A000379, A064547, A368407.

Analogous to A275508.

Programs

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]

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};