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

0,1

Links

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

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 *)

Crossrefs

Cf. A000040, A007442, A111107.

Sequence in context: A334276 A055496 A105120 * A084403 A261201 A055011

Adjacent sequences: A384671 A384672 A384673 * A384675 A384676 A384677

Keyword

nonn

Author

Alexander R. Povolotsky, Jun 06 2025

Extensions

More terms from Alois P. Heinz, Jun 06 2025

Status

approved