A093086 -id:A093086 - cp's OEIS frontend

A339379 Irregular triangle read by rows; the first row simply contains the value 1; given the succession of digits of the n-th row, say [d_0, ..., d_k], the (n+1)-th row is the succession of digits of [d_0, d_0+d_1, d_1+d_2, ..., d_{k-1}+d_k, d_k].

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

Offset: 0

Rémy Sigrist, Dec 02 2020

This sequence combines features of Pascal's triangle (A007318) and of A093086.
Rows 0 to 4 match that of Pascal's triangle, thereafter the values differ.
Every column is eventually periodic.

			The first rows are:
    1
    1, 1
    1, 2, 1
    1, 3, 3, 1
    1, 4, 6, 4, 1
    1, 5, 1, 0, 1, 0, 5, 1
    1, 6, 6, 1, 1, 1, 5, 6, 1
    1, 7, 1, 2, 7, 2, 2, 6, 1, 1, 7, 1
    1, 8, 8, 3, 9, 9, 4, 8, 7, 2, 8, 8, 1
    1, 9, 1, 6, 1, 1, 1, 2, 1, 8, 1, 3, 1, 2, 1, 5, 9, 1, 0, 1, 6, 9, 1

Alois P. Heinz, Rows n = 0..30, flattened

See A339359 for a similar sequence.

Cf. A007318, A093086.

NestList[Flatten[IntegerDigits[Map[Total, Partition[#, 2, 1, {-1, 1}, 0]]]] &, {1}, 10] (* Paolo Xausa, Aug 19 2025 *)

{ r = [1]; for (n=0, 9, apply (v -> print1 (v ", "), r); d = concat(apply(v -> if (v, digits(v), [0]), r)); r = concat(apply(v -> if (v, di
gits(v), [0]), vector(#d+1, k, if (k==1, d[k], k==#d+1, d[#d], d[k-1]+d[k]))))) }

A093100 "Lucas-digits": start with "13", append sum of first 2 digits to the preceding number, drop first digit.

Original entry on oeis.org

13, 34, 47, 711, 118, 182, 829, 2910, 91011, 101110, 11101, 11012, 10122, 1221, 2213, 2134, 1343, 3434, 4347, 3477, 4777, 77711, 771114, 7111414, 1114148, 1141482, 1414822, 4148225, 1482255, 4822555, 82255512, 225551210, 255512104, 555121047

Offset: 1

Bodo Zinser, Mar 22 2004

There are only 7 primes in the first 1000 terms of this sequence. The first 6 primes are 13, 47, 829, 2213, 77711, and 174111811681183993. The 7th prime, a(920), has 214 digits. - Harvey P. Dale, Aug 04 2014

			a(4): sum of first 2 digits of a(3)=11, append 11 to 47 and get 4711, drop first digit and get 711.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A093086-A093099.

ld[n_]:=Module[{idn=IntegerDigits[n]},FromDigits[Rest[Join[ idn, IntegerDigits[ Total[ Take[idn,2]]]]]]]; NestList[ld,13,40] (* Harvey P. Dale, Aug 04 2014 *)

A105967 Slowest increasing sequence all of whose successive digits are the digits of the Fibonacci numbers.

Original entry on oeis.org

0, 11, 23, 58, 132, 134, 558, 914, 4233, 3776, 10987, 15972, 58441, 81676, 510946, 1771128, 6574636, 8750251, 21393196, 41831781, 151422983, 204013462

Offset: 0

Alexandre Wajnberg, Apr 28 2005

Ron Knott, Fibonacci Numbers.

Cf. A093086, A102085, A098080.

Write down the Fibonacci numbers and consider it as a unique succession of digits. Divide up into chunks of minimal length (and not beginning with 0) so that chunks are increasing numbers in order to form the slowest ever increasing sequence of slices (disregarding the number of digits) of the succession of the digits of the Fibonacci numbers.

A093093 "Fibonacci in digits - up and down": start with a(1)=1, a(2)=1; repeatedly adjoin either the sum of the two previous terms (if that sum happens to be odd) or else adjoin digits of the sum of previous two terms (if that sum happens to be even).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 3, 4, 2, 4, 7, 6, 6, 11, 13, 1, 2, 17, 2, 4, 1, 4, 3, 19, 19, 6, 5, 5, 7, 2, 2, 3, 8, 25, 11, 1, 0, 1, 2, 9, 4, 5, 11, 33, 3, 6, 1, 2, 1, 1, 3, 11, 13, 9, 1, 6, 4, 4, 3, 6, 9, 7, 3, 3, 2, 4, 1, 4, 2, 4, 2, 2, 1, 0, 7, 1, 0, 8, 7, 9, 15, 1, 6, 1, 0, 6, 5, 6, 5, 5, 6, 6, 6, 4, 3, 1, 7

Offset: 1

Bodo Zinser, Mar 20 2004

			... a(8)=a(6)+a(7), a(9)=left digit of (a(7)+a(8)=13+21=3 4) as 34 is even, a(10)=right digit of (a(7)+a(8)=13+21=3 4) as 34 is even, a(13)=a(9)+a(10) as odd, ...

Cf. A093086 to A093092.

cp's OEIS Frontend

A339379 Irregular triangle read by rows; the first row simply contains the value 1; given the succession of digits of the n-th row, say [d_0, ..., d_k], the (n+1)-th row is the succession of digits of [d_0, d_0+d_1, d_1+d_2, ..., d_{k-1}+d_k, d_k].

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A093100 "Lucas-digits": start with "13", append sum of first 2 digits to the preceding number, drop first digit.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A105967 Slowest increasing sequence all of whose successive digits are the digits of the Fibonacci numbers.

Views

Author

Keywords

Links

Crossrefs

Formula

A093093 "Fibonacci in digits - up and down": start with a(1)=1, a(2)=1; repeatedly adjoin either the sum of the two previous terms (if that sum happens to be odd) or else adjoin digits of the sum of previous two terms (if that sum happens to be even).

Views

Author

Keywords

Examples

Crossrefs