cp's OEIS Frontend

A177711 Natural numbers which are not sums of one or more distinct primorials.

%I A177711 #13 Feb 17 2025 12:00:40
%S A177711 4,5,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,34,
%T A177711 35,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,
%U A177711 62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85
%N A177711 Natural numbers which are not sums of one or more distinct primorials.
%C A177711 Numbers with a digit larger than one in primorial base representation, A049345. Numbers k for which A276086(k) is not squarefree. - _Antti Karttunen_, Feb 17 2025
%H A177711 Antti Karttunen, <a href="/A177711/b177711.txt">Table of n, a(n) for n = 1..20000</a>
%H A177711 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A177711 COMPLEMENT of {Primorial numbers A002110 UNION A177689 Sums of 2 distinct primorials UNION Sums of 3 distinct primorials A177697 UNION Sums of 4 distinct primorials A177709 UNION ...}.
%F A177711 {k such that A328114(k) > 1}. - _Antti Karttunen_, Feb 17 2025
%e A177711 1 and 2 are not in the sequence, as they are the first and second primorials, 0# and 1#. 3 is not in the sequence, as 3 = 1+2. Neither 4 nor 5 can be the sum of distinct primorials (i.e. 4=2+2 or 5 = 2+2+1 repeat a primorial). 6 is not in the sequence, as it is 3#. 7 and 8 are not in the sequence as 7 = 6+1 and 8 = 6+2. 9 is not in the sequence, as 9 = 6+2+1.
%o A177711 (PARI) is_A177711(n) = { my(p=2); while(n, if(n%p > 1, return(1)); n = n\p; p = nextprime(1+p)); (0); }; \\ _Antti Karttunen_, Feb 17 2025
%Y A177711 Cf. A002110, A049345, A177689, A177697, A177708, A177709, A276086.
%Y A177711 Complement of A276156.
%Y A177711 Positions of terms > 1 in A328114.
%Y A177711 Subsequences: A380535, A381034.
%K A177711 easy,nonn
%O A177711 1,1
%A A177711 _Jonathan Vos Post_, May 11 2010