A062062 Smallest increasing sequence where each term is coprime to preceding three terms.

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

Author

Amarnath Murthy, Jun 12 2001

Keywords

• nonn
• easy

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

Examples

			After 19, 22, 23 the next term is 25 as 24 has 2 as common divisor with 22.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• 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.

Crossrefs

Cf. A047255, A062063.

Programs

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 ]

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

Extensions

More terms from Erich Friedman, Jun 15 2001

Clarified by Charles R Greathouse IV, Aug 02 2010