A390831 - OEIS

%I #15 Nov 29 2025 10:12:32

%S 1,3,8,3,29,35,18,181,348,160,117,962,623,322,1858,1620,1766,3805,

%T 7224,9750,5791,37943,59154,27100,97583,61986,125112,130775,163947,

%U 243437,480984,627486,473240,1461949,2675131,2063109,2623502,1680273,8040568,2970378,4191532

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

%e 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.

%e 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.

%t 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 *)

%o (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

%Y Cf. A080082, A081411, A389823.

%K nonn

%O 1,2

%A _Michel Marcus_, Nov 21 2025

%E a(16)-a(21) from _Amiram Eldar_, Nov 21 2025

%E a(22)-a(41) from _Jinyuan Wang_, Nov 28 2025