A390831 Numbers of terms of 1+A081411 that are divisible by prime(n).

1, 3, 8, 3, 29, 35, 18, 181, 348, 160, 117, 962, 623, 322, 1858, 1620, 1766, 3805, 7224, 9750, 5791, 37943, 59154, 27100, 97583, 61986, 125112, 130775, 163947, 243437, 480984, 627486, 473240, 1461949, 2675131, 2063109, 2623502, 1680273, 8040568, 2970378, 4191532

Offset

1,2

Links

Table of n, a(n) for n=1..41.

Example

For n=2, a(2)=3 because there are only 3 terms of 1+A081411 divisible by prime(2)=3; they are 3, 33, 129 at indices 2, 5, 6.
For n=3, a(3)=8 because there are only 8 terms of 1+A081411 divisible by prime(3)=5; they are at indices 3, 8, 9, 13, 22, 23, 27, 33.

Mathematica

seq[numprimes_] := Module[{d = Differences[Prime[Range[numprimes]]], ps, ind, np, s, primes, r = 1}, ps = Union[Flatten[Map[FactorInteger[#][[;; , 1]] &, Select[Union[d], # > 1 &]]]]; ind = PrimePi[ps]; np = First @ Complement[Range[ind[[-1]] + 1], ind] - 1; s = Table[0, {np}]; primes = Prime[Range[np]]; Do[r *= d[[i]]; Do[If[Divisible[r + 1, ps[[j]]], s[[j]]++], {j, 1, np}], {i, 1, Length[d]}]; s]; seq[10^5] (* Amiram Eldar, Nov 21 2025 *)

Prog

(PARI) a(n) = my(c=0, p=2, r=Mod(1, prime(n))); forprime(q=3, oo, r*=(q-p); if(r==-1, c++); if(r==0, return(c)); p=q); \\ Jinyuan Wang, Nov 28 2025

Crossrefs

Cf. A080082, A081411, A389823.

Sequence in context: A322360 A392089 A392087 * A058936 A280369 A280979

Adjacent sequences: A390828 A390829 A390830 * A390832 A390833 A390834

Keyword

nonn

Author

Michel Marcus, Nov 21 2025

Extensions

a(16)-a(21) from Amiram Eldar, Nov 21 2025

a(22)-a(41) from Jinyuan Wang, Nov 28 2025

Status

approved