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

1,1

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to primorial base.

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

Example

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.

Prog

(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

Crossrefs

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

Complement of A276156.

Positions of terms > 1 in A328114.

Subsequences: A380535, A381034.

Sequence in context: A327577 A092961 A327614 * A115945 A092027 A084750

Adjacent sequences: A177708 A177709 A177710 * A177712 A177713 A177714

Keyword

easy,nonn

Author

Jonathan Vos Post, May 11 2010

Status

approved