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A079696 Numbers one more than composite numbers. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)