A374908 Each term is the sum of the preceding term and its seven-segment total A006942.

0, 6, 12, 19, 27, 35, 45, 54, 63, 74, 81, 90, 102, 115, 124, 135, 147, 156, 169, 183, 197, 208, 226, 242, 256, 272, 285, 302, 318, 332, 347, 359, 375, 388, 407, 420, 435, 449, 463, 478, 492, 507, 521, 533, 548, 564, 579, 593, 609, 627, 641, 653, 669, 687, 703

Offset: 0

Author

David J. Ellis, Jul 23 2024

Keywords

• nonn
• base
• easy

Comments

The number of segments in each digit 0 to 9 is [6,2,5,5,4,5,6,3,7,6].

Conjecture: Taking the least significant digit of each term is not an eventually periodic sequence.

Examples

			For n=1, the preceding a(0) = 0 is 6 segments so that a(1) = 0 + 6 = 6.
		

Links

• Dominic McCarty, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006942, A219675.

Programs

Mathematica

s={0};Do[AppendTo[s,Last[s]+ Plus @@ (IntegerDigits@ Last[s] /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 3, 8 -> 7, 9 -> 6})],{n,54}];s (* James C. McMahon, Aug 19 2024 *)

Python

from itertools import islice
def b(n): return sum([6, 2, 5, 5, 4, 5, 6, 3, 7, 6][int(d)] for d in str(n))
def agen(): # generator of terms
    yield (an:=0)
    while True: yield (an:=an+b(an))
print(list(islice(agen(), 55))) # Michael S. Branicky, Jul 28 2024

Formula

a(n) = a(n-1) + A006942(a(n-1)).