A277197 First differences of A260443.

1, 1, 3, -1, 13, -3, 15, -23, 83, -15, 195, -235, 415, -345, 105, -199, 619, -105, 6225, -6505, 20005, -17625, 6825, -9373, 15673, -12075, 43575, -46865, 21665, -20895, 1155, -2297, 6917, -1155, 324975, -328055, 3541055, -3415125, 1525125, -1652903, 4960403, -4318125, 52513125, -53137385, 24787385, -24604125, 525525, -727507, 1212607, -929775, 57598275

Offset: 0

Author

Antti Karttunen, Oct 10 2016

Keywords

• sign
• look

Comments

Two observations (not yet proved): from n=3 onward each term is alternatively negative and positive, and from n=4 onward the terms a(2n-1) and a(2n) seem to have at least the rightmost digit same in their decimal representation.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..1024

Crossrefs

Cf. A260443.

Cf. also A277198.

Programs

Mathematica

a[n_] := a[n] = Which[n < 2, n + 1, EvenQ@ n, Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1] &@ a[n/2], True, a[#] a[# + 1] &[(n - 1)/2]]; Differences@ Table[a@ n, {n, 0, 51}] (* Michael De Vlieger, Apr 05 2017 *)

Scheme

(define (A277197 n) (- (A260443 (+ 1 n)) (A260443 n)))

Formula

a(n) = A260443(n+1) - A260443(n).