A061728 Start with (a, b) = (2, 4). The next pair (a', b') is ((b + 1) mod 10, (a + 1) mod 10) where (a, b) is the previous pair.

2, 4, 5, 3, 4, 6, 7, 5, 6, 8, 9, 7, 8, 0, 1, 9, 0, 2, 3, 1, 2, 4, 5, 3, 4, 6, 7, 5, 6, 8, 9, 7, 8, 0, 1, 9, 0, 2, 3, 1, 2, 4, 5, 3, 4, 6, 7, 5, 6, 8, 9, 7, 8, 0, 1, 9, 0, 2, 3, 1, 2, 4, 5, 3, 4, 6, 7, 5, 6, 8, 9, 7, 8, 0, 1, 9, 0, 2, 3, 1, 2, 4, 5, 3, 4, 6, 7, 5, 6, 8, 9, 7, 8, 0, 1, 9, 0, 2, 3, 1, 2, 4, 5, 3, 4

Offset

1,1

Comments

Has period 20.

References

Norman Sullivan, Test Your Own IQ, Workman Publishing Co. New York, NY, 1994, pp. 49, 51.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1).

Formula

From Colin Barker, Jul 02 2018: (Start)

G.f.: x*(2 + 2*x + 3*x^2 + 4*x^4 + 2*x^5 + 5*x^6 + 6*x^8 + 2*x^9 + 7*x^10 + 8*x^12 - 8*x^13 + 9*x^14 + 2*x^17 + x^18) / ((1 - x)*(1 + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)*(1 - x^2 + x^4 - x^6 + x^8)).

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11) - a(n-12) + a(n-13) - a(n-14) + a(n-15) - a(n-16) + a(n-17) - a(n-18) + a(n-19) for n>19.

(End)

a(1) = 2, a(2) = 4. {a(n+1), a(n+2)} = (1 + {a(n), a(n - 1)}) mod 10. - Michael De Vlieger, Jul 01 2018

a(n) = (2*floor(n/4) + floor(3*(n mod 4)/2) + 1) mod 10. - Jon E. Schoenfield, Jul 01 2018

Example

24 (42)-> 53, (35)-> 46, (64)-> 75.

Mathematica

Nest[Append[#, Mod[1 + {#2, #1}, 10] & @@ #[[-1]]] &, {{2, 4}}, 42] // Flatten (* Michael De Vlieger, Jul 01 2018 *)

Prog

(PARI) { f="b061728.txt"; for (n=1, 500, if (n==1, a=2; b=4, s=a; a=(b + 1)%10; b=(s + 1)%10); write(f, 2*n - 1, " ", a); write(f, 2*n, " ", b) ) } \\ Harry J. Smith, Jul 27 2009
(PARI) Vec(x*(2 + 2*x + 3*x^2 + 4*x^4 + 2*x^5 + 5*x^6 + 6*x^8 + 2*x^9 + 7*x^10 + 8*x^12 - 8*x^13 + 9*x^14 + 2*x^17 + x^18) / ((1 - x)*(1 + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)*(1 - x^2 + x^4 - x^6 + x^8)) + O(x^150)) \\ Colin Barker, Jul 02 2018

Crossrefs

Cf. A061729.

Sequence in context: A071286 A021807 A284561 * A332017 A276127 A182115

Adjacent sequences: A061725 A061726 A061727 * A061729 A061730 A061731

Keyword

nonn,easy,base

Author

Jason Earls, May 06 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001

Offset changed from 24 to 1 by Harry J. Smith, Jul 27 2009

Name edited by David A. Corneth and Jon E. Schoenfield, Jul 05 2018

Edited by N. J. A. Sloane, Jul 06 2018

Status

approved