A262951 a(1) = 1, a(2) = 3, a(3) = 4 and for n>=4, a(n) = (a(n-3)+a(n-2)+a(n-1)+k) mod 10 where k = a(n/6) if n is divisible by 6, else 0.

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

Offset

1,2

Comments

This sequence is similar to A130893. Every term of index k is the sum of the 3 preceding terms modulo 10, except that for every sixth term the sum includes also the term of index k/6.

Lambert gave this sequence in Anlage zur Architectonic as a kind of early pseudorandom sequence. - Charles R Greathouse IV, Oct 05 2015

Links

Table of n, a(n) for n=1..87.

Maarten Bullynck, L’histoire de l’informatique et l’histoire des mathématiques : rencontres, opportunités et écueils, Images des Mathématiques, CNRS, 2015 (in French).

Johann Heinrich Lambert, Anlage zur Architectonic, oder Theorie des Einfachen und des Ersten in der philosophischen und mathematischen Erkenntniß, 1771.

Index entries for sequences related to pseudo-random numbers.

Formula

a(n) = (a(n-3) + a(n-2) + a(n-1)) mod 10 if n is not a multiple of 6.

a(n) = (a(n-3) + a(n-2) + a(n-1) + a(n/6)) mod 10 if n is a multiple of 6.

Example

a(6) = 4+8+5 = (17 + a(6/6)) mod 10 = (17 + 1) mod 10 = 8.

Prog

(PARI) lista(nn) = {va = vector(nn); va[1] = 1; va[2] = 3; va[3] = 4; for (k=4, nn, va[k] = va[k-3] + va[k-2] + va[k-1]; if (! (k % 6) && (k > 6), va[k] += va[k/6]); va[k] = va[k] % 10; ); va; }

Crossrefs

Cf. A130893.

Sequence in context: A245598 A340533 A050274 * A288091 A057926 A078766

Adjacent sequences: A262948 A262949 A262950 * A262952 A262953 A262954

Keyword

nonn

Author

Michel Marcus, Oct 05 2015

Status

approved