A368407 a(n) is the least start of a run of exactly n consecutive integers with an odd number of Fermi-Dirac factors (A064547).

7, 16, 23, 2, 101, 135, 429, 227, 5018, 2682, 1692, 819, 184170, 175683, 93597, 117032, 300773, 466065, 2012413, 2177318, 10267248, 39069334, 25085909, 3829812, 132899228, 316564239, 391031618, 53858226, 355227517, 1484451701, 18503618566, 370565617, 52188004547, 5708850192

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Mathematica

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]

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

Cf. A000028, A064547, A368408.

Analogous to A275509.

Sequence in context: A044059 A287369 A342743 * A044440 A114556 A136772

Adjacent sequences: A368404 A368405 A368406 * A368408 A368409 A368410

Keyword

nonn,base

Author

Amiram Eldar, Dec 23 2023

Status

approved