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

4, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 34, 35, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85

Offset: 1

Author

Jonathan Vos Post, May 11 2010

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A002110, A049345, A177689, A177697, A177708, A177709, A276086.

Complement of A276156.

Positions of terms > 1 in A328114.

Subsequences: A380535, A381034.

Programs

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

Formula

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 ...}.

{k such that A328114(k) > 1}. - Antti Karttunen, Feb 17 2025