A079696 Numbers one more than composite numbers.

5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96

Offset

1,1

Comments

From Hieronymus Fischer, Mar 27 2014: (Start)

Numbers m such that m == 1 mod j and m > j^2 for any j > 1.

Example: m == 6 mod 10 is a term for m > 6, since m = 6 + 10k = 1 + (2k+1)*5, and m > (2k+1)^2 (for k := 1, m = 16), and m > 5^2 (for k > 1, m > 16).

A187813 and this sequence have no terms in common; this means that for each term a(n) there exists a base b such that the base-b digit sum is b.

Example: m = 1 + 3k, k > 3, is a term, since m > 3(1+3) > 3^2, thus the base-b-digit sum of (m) is = b for any b > 1 (here the base b is k+1 since 1+3k = 2(k+1) + k-1).

In general: Given a term a(n) there are p and q with p >= q > 1 such that a(n) = 1 + p*q. With b := p + 1 we get a(n) = (q-1)*b + b - (q-1), where 1 <= q-1 < b, which implies that the base-b digital sum of a(n) is = q-1 + b - (q-1) = b.

This sequence is the complement of the disjunction of A187813 with A239708. This means that a number m is a term if and only if there is a base b > 2 such that the base-b digit sum of m is b.

(End)

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Formula

a(n) = A002808(n) + 1.

A239703(a(n)) > 0. - Hieronymus Fischer, Apr 10 2014

Crossrefs

Cf. A072668.

Cf. A007953, A187813, A239703, A239708.

Sequence in context: A160811 A116451 A126949 * A275718 A129270 A153031

Adjacent sequences: A079693 A079694 A079695 * A079697 A079698 A079699

Keyword

nonn,easy

Author

Vladeta Jovovic, Jan 31 2003

Extensions

Edited by Charles R Greathouse IV, Mar 19 2010

Status

approved