A384674 Lexicographically smallest sequence of distinct primes whose inverse binomial transform consists only of primes.

2, 5, 11, 23, 47, 97, 211, 491, 1187, 2857, 6659, 14879, 31891, 65929, 132469, 261059, 510031, 999721, 1988797, 4048339, 8450557, 18014701, 38902439, 84347189, 182269327, 390630769, 828123239, 1735146097, 3594509969, 7369765889, 14975024861, 30200498591, 60537295711

Offset: 0

Author

Alexander R. Povolotsky, Jun 06 2025

Keywords

• nonn
• changed

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A007442, A111107.

Programs

Maple

a:= proc(n) option remember; local b, p;
      b:= add(a(n-i)*binomial(n, i)*(-1)^i, i=1..n);
      p:= nextprime(abs(b));
      do if isprime(p+b) then break fi ;
         p:= nextprime(p)
      od; p
    end: a(0):=2:
seq(a(n), n=0..32);  # Alois P. Heinz, Jun 06 2025

Mathematica

a[n_] := a[n] = Module[{b, p}, b = Sum[a[n-i]*Binomial[n, i]*(-1)^i, {i, 1, n}]; p = NextPrime[Abs[b]]; While[True, If[PrimeQ[p+b], Break[]]; p = NextPrime[p]]; p];
a[0] = 2;
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Aug 28 2025, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Jun 06 2025