A069563 a(1) = 1, a(2) = 4; for n > 2, a(n) = k*a(n-1) + 1 where k is smallest number > 1 such that k*a(n-1) + 1 is a multiple of n.

1, 4, 9, 28, 85, 426, 3409, 23864, 167049, 1837540, 18375401, 128627808, 1157650273, 10418852458, 83350819665, 1250262294976, 22504721309569, 382580262262674, 4973543409414763, 64656064322391920

Offset

1,2

Comments

There is no solution to k * 64656064322391920 + 1 = 0 (mod 21). - Sean A. Irvine, May 04 2024

Links

Table of n, a(n) for n=1..20.

Example

a(6) = 426, a(7) = 3409 since 3409 = 8*426 + 1 is a multiple of 7.

Mathematica

a[1] = 1; a[n_] := a[n] = Module[{k}, If[ Intersection[ Transpose[ FactorInteger[a[n - 1]]] [[1]], Transpose[ FactorInteger[n]] [[1]]] == {}, k = 2; While[ !IntegerQ[(k*a[n - 1] + 1)/n], k++ ]; Return[ k*a[n - 1] + 1], k = 1; While[ !IntegerQ[(k*a[n - 2] + 1)/n], k++ ]; Return[ k*a[n - 2] + 1]]]; Table[ a[n], {n, 1, 23}]

Crossrefs

Sequence in context: A232765 A094255 A192234 * A352878 A276984 A210969

Adjacent sequences: A069560 A069561 A069562 * A069564 A069565 A069566

Keyword

nonn,fini,full,changed

Author

Amarnath Murthy, Mar 23 2002

Extensions

More terms from Sascha Kurz, Mar 23 2002

Edited, corrected and extended by Robert G. Wilson v, Apr 12 2002

Incorrect a(21) removed by Sean A. Irvine, May 04 2024

Status

approved