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

%I A384674 #26 Aug 28 2025 10:20:51
%S A384674 2,5,11,23,47,97,211,491,1187,2857,6659,14879,31891,65929,132469,
%T A384674 261059,510031,999721,1988797,4048339,8450557,18014701,38902439,
%U A384674 84347189,182269327,390630769,828123239,1735146097,3594509969,7369765889,14975024861,30200498591,60537295711
%N A384674 Lexicographically smallest sequence of distinct primes whose inverse binomial transform consists only of primes.
%H A384674 Alois P. Heinz, <a href="/A384674/b384674.txt">Table of n, a(n) for n = 0..1000</a>
%p A384674 a:= proc(n) option remember; local b, p;
%p A384674       b:= add(a(n-i)*binomial(n, i)*(-1)^i, i=1..n);
%p A384674       p:= nextprime(abs(b));
%p A384674       do if isprime(p+b) then break fi ;
%p A384674          p:= nextprime(p)
%p A384674       od; p
%p A384674     end: a(0):=2:
%p A384674 seq(a(n), n=0..32);  # _Alois P. Heinz_, Jun 06 2025
%t A384674 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];
%t A384674 a[0] = 2;
%t A384674 Table[a[n], {n, 0, 32}] (* _Jean-François Alcover_, Aug 28 2025, after _Alois P. Heinz_ *)
%Y A384674 Cf. A000040, A007442, A111107.
%K A384674 nonn,changed
%O A384674 0,1
%A A384674 _Alexander R. Povolotsky_, Jun 06 2025
%E A384674 More terms from _Alois P. Heinz_, Jun 06 2025