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A062062
Smallest increasing sequence where each term is coprime to preceding three terms.
4
1, 2, 3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 22, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 41, 43, 44, 45, 47, 49, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 67, 69, 71, 73, 74, 75, 77, 79, 82, 83, 85, 87, 88, 89, 91, 93, 94, 95, 97, 99, 101, 103, 104, 105, 107, 109, 113
OFFSET
1,2
COMMENTS
a(n+125) = a(n) + 210, n >= 7. Also maximal term difference is 4 = a(68)-a(67). - David W. Wilson, Jun 18 2001
LINKS
Hsien-Kuei Hwang, Mihyun Kang, Guan-Huei Duh, Asymptotic Expansions for Sub-Critical Lagrangean Forms, LIPIcs Proceedings of Analysis of Algorithms 2018, Vol. 110. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2018.
EXAMPLE
After 19, 22, 23 the next term is 25 as 24 has 2 as common divisor with 22.
MATHEMATICA
a[ 1 ]=1; a[ 2 ]=2; a[ 3 ]=3; a[ n_ ] := a[ n ]=Module[ {}, b=a[ n-1 ]; While[ GCD[ b, a[ n-1 ] ]>1||GCD[ b, a[ n-2 ] ]> 1||GCD[ b, a[ n-3 ] ]>1, b++ ]; b ] Array[ a, 100 ]
PROG
(PARI) { for (n=1, 1000, if (n>3, until (gcd(a, a1)==1 && gcd(a, a2)==1 && gcd(a, a3)==1, a++); a3=a2; a2=a1; a1=a, if (n==1, a=a3=1, if (n==2, a=a2=2, a=a1=3))); write("b062062.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 31 2009
CROSSREFS
Sequence in context: A039019 A359028 A047255 * A256133 A078643 A137698
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Jun 12 2001
EXTENSIONS
More terms from Erich Friedman, Jun 15 2001
Clarified by Charles R Greathouse IV, Aug 02 2010
STATUS
approved