cp's OEIS Frontend

A094044 Alternate prime and nonprime numbers not included earlier such that every concatenation of a pair of terms is a prime: a(2n) is nonprime and a(2n-1) is prime.

%I A094044 #8 Oct 25 2017 05:13:07
%S A094044 2,9,7,1,3,49,19,33,13,21,11,51,47,87,31,63,17,77,23,39,29,27,41,57,
%T A094044 37,69,59,81,61,99,67,91,73,93,43,117,79,111,71,119,53,129,83,177,89,
%U A094044 123,113,143,107,171,103,141,97,159,157,133,109,121,139,169,151,153,137,147
%N A094044 Alternate prime and nonprime numbers not included earlier such that every concatenation of a pair of terms is a prime: a(2n) is nonprime and a(2n-1) is prime.
%C A094044 Conjecture: all members of A045572 are in the sequence. - _Robert Israel_, Oct 24 2017
%H A094044 Robert Israel, <a href="/A094044/b094044.txt">Table of n, a(n) for n = 1..10000</a>
%e A094044 a(3)=7 => 97 is a prime but not necessarily 297 (in fact not a prime).
%p A094044 N:= 1000: # to get terms before the first term > N
%p A094044 P, C:= selectremove(isprime, [1,$3..N]):
%p A094044 dcat:= proc(x,y) 10^(1+ilog10(y))*x+y end proc:
%p A094044 A[1]:= 2:
%p A094044 for n from 2 do
%p A094044   if n::even then
%p A094044     for j from 1 to nops(C) do
%p A094044       if isprime(dcat(A[n-1],C[j])) then
%p A094044          A[n]:= C[j];
%p A094044          C:= subsop(j=NULL,C);
%p A094044          break
%p A094044       fi
%p A094044     od
%p A094044   else
%p A094044     for j from 1 to nops(P) do
%p A094044       if isprime(dcat(A[n-1],P[j])) then
%p A094044         A[n]:= P[j];
%p A094044         P:= subsop(j=NULL,P);
%p A094044         break
%p A094044       fi
%p A094044     od
%p A094044   fi;
%p A094044   if not assigned(A[n]) then break fi
%p A094044 od:
%p A094044 seq(A[i],i=1..n-1); # _Robert Israel_, Oct 24 2017
%t A094044 p = Prime[ Range[ 500]]; np = Drop[ Complement[ Range[ 500], p], 1]; a[0] = 0; a[n_] := a[n] = Block[{k = 1, q = IntegerDigits[a[n - 1]]}, If[ OddQ[n], While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ p[[k]] ]]]], k++ ]; q = p[[k]]; p = Delete[p, k]; q, While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ np[[k]] ]]]], k++ ]; q = np[[k]]; np = Delete[np, k]; q]]; Table[ a[n], {n, 64}]
%Y A094044 Cf. A088614, A094045.
%K A094044 nonn,base
%O A094044 1,1
%A A094044 _Robert G. Wilson v_, Apr 23 2004