A062063 a(n) is the smallest number greater than a(n-1) that is coprime to the last four terms of the sequence, with a(1) = 1, a(2) = 2, a(3) = 3, and a(4) = 5.

1, 2, 3, 5, 7, 11, 13, 16, 17, 19, 21, 23, 25, 26, 29, 31, 33, 35, 37, 38, 41, 43, 45, 47, 49, 52, 53, 55, 57, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 81, 83, 85, 86, 89, 91, 93, 95, 97, 101, 103, 104, 105, 107, 109, 113, 116, 117, 119, 121, 125, 127, 128, 129

Offset: 1

Author

Amarnath Murthy, Jun 12 2001

Keywords

• nonn

Comments

Is a(n+1) - a(n) bounded?

For n < 10^7, the maximum value of a(n+1) - a(n) is 12. - T. D. Noe, May 14 2007

The first differences appear to be periodic with period 245589; this should lead to a proof that the first differences are bounded. If the pattern holds through a(189103530) then it is proved; it suffices to work mod 2310. - Charles R Greathouse IV, Dec 19 2011

Links

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

Crossrefs

Cf. A047255, A062062.

Programs

PARI

{ for (n=1, 1000, if (n>4, until (gcd(a, a1)==1 && gcd(a, a2)==1 && gcd(a, a3)==1 && gcd(a, a4)==1, a++); a4=a3; a3=a2; a2=a1; a1=a, if (n==1, a=a4=1, if (n==2, a=a3=2, if (n==3, a=a2=3, a=a1=5)))); write("b062063.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 31 2009

Extensions

Corrected and extended by Dean Hickerson, Jul 10 2001