A368407 - OEIS

%I #6 Dec 24 2023 02:44:02

%S 7,16,23,2,101,135,429,227,5018,2682,1692,819,184170,175683,93597,

%T 117032,300773,466065,2012413,2177318,10267248,39069334,25085909,

%U 3829812,132899228,316564239,391031618,53858226,355227517,1484451701,18503618566,370565617,52188004547,5708850192

%N a(n) is the least start of a run of exactly n consecutive integers with an odd number of Fermi-Dirac factors (A064547).

%t q[n_] := OddQ[Sum[DigitCount[e, 2, 1], {e, FactorInteger[n][[;;, 2]]}]]; q[1] = False; 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]

%o (PARI) is(n) = {my(e = factor(n)[, 2]); sum(i = 1, #e, hammingweight(e[i])) % 2;}

%o 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};

%Y Cf. A000028, A064547, A368408.

%Y Analogous to A275509.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Dec 23 2023