

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
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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 baseb digit sum is b.
Example: m = 1 + 3k, k > 3, is a term, since m > 3(1+3) > 3^2, thus the basebdigit sum of (m) is = b for any b > 1 (here the base b is k+1 since 1+3k = 2(k+1) + k1).
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) = (q1)*b + b  (q1), where 1 <= q1 < b, which implies that the baseb digital sum of a(n) is = q1 + b  (q1) = 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 baseb 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



