A076368 a(1) = 1; for n > 1, a(n) = prime(n) - prime(n-1) + 1.

1, 2, 3, 3, 5, 3, 5, 3, 5, 7, 3, 7, 5, 3, 5, 7, 7, 3, 7, 5, 3, 7, 5, 7, 9, 5, 3, 5, 3, 5, 15, 5, 7, 3, 11, 3, 7, 7, 5, 7, 7, 3, 11, 3, 5, 3, 13, 13, 5, 3, 5, 7, 3, 11, 7, 7, 7, 3, 7, 5, 3, 11, 15, 5, 3, 5, 15, 7, 11, 3, 5, 7, 9, 7, 7, 5, 7, 9, 5, 9, 11, 3, 11, 3, 7, 5, 7, 9, 5, 3, 5, 13, 9, 5, 9, 5, 7

Offset: 1

Author

Labos Elemer, Oct 14 2002

Keywords

• nonn

Comments

Number of occurrences of n in A060646 or n-th prime in A076367.

Sequences A060646, A076367, A076368 were used in proving a property of 30. See A048597, A060646 and corresponding References. It is provable [Bonse] that a(n)>=3 if n>3.

For n>1, a(n) is the sum of the digits of prime(n) in the base prime(n-1). - R. J. Cano, Dec 31 2016; corrected by Michel Marcus, Jan 01 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• H. Bonse, Über eine bekannte Eigenshaft der Zahl 30 und ihre Verallgemeinerung, Archiv d. Math. u. Physik (3) vol. 12 (1907) 292-295.

Crossrefs

Cf. A048597, A060646, A076367. See also A076366.

Cf. A000040, A001223.

Programs

Magma

[1] cat [NthPrime(n)-NthPrime(n-1)+1: n in [1..80]]; // Vincenzo Librandi, Jan 01 2017

Mathematica

c[x_, j_] := x+1-(j+Prime[j])c[x, 0]=x; a=1000; t=Table[0, {a}]; t1=Table[0, {a}]; Table[fl=1; (*Print["% ", u, " #"]; *)Do[s=c[u, n]; If[Equal[fl, 1]&&Equal[Sign[s], -1], Print[n]; t[[u]]=n; t1[[u]]=Prime[n]; fl=0], {n, 1, u}], {u, 1, a}]//t (*=A060646*)//t1 (*=A076367*) Table[Count[t, j], {j, 1, PrimePi[a]}]
(* Second program *)
Table[If[n == 1, 1, (Prime@ n - Prime[n - 1]) + 1], {n, 97}] (* Michael De Vlieger, Dec 31 2016 *)
Join[{1},Differences[Prime[Range[100]]]+1] (* Harvey P. Dale, Mar 13 2019 *)

Extensions

Simpler description from Vladeta Jovovic, Mar 29 2003