A332562 a(n) = number formed by concatenating the decimal digits of 44, 45, 46, ..., 44+n.

44, 4445, 444546, 44454647, 4445464748, 444546474849, 44454647484950, 4445464748495051, 444546474849505152, 44454647484950515253, 4445464748495051525354, 444546474849505152535455, 44454647484950515253545556, 4445464748495051525354555657

Offset: 0

Author

Scott R. Shannon and N. J. A. Sloane, Feb 24 2020

Keywords

• nonn
• base

Comments

This is an instance of a sequence arising in A332580.

As of Feb 24 2020, it is an open question as to whether there is an N such that a(N) is divisible by 44+N+1. If such an N exists, N > 10^11, as shown by Joseph Myers (see A332580).

We have now shown that N = 2783191412912. See A332580 and the attached paper. - N. J. A. Sloane, Apr 28 2020

Links

• Robert Israel, Table of n, a(n) for n = 0..350
• J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020.

Crossrefs

Cf. A332580.

Programs

Magma

[Seqint(Reverse(&cat[Reverse(Intseq(k)): k in [44..n]])): n in [44..60]]; // Vincenzo Librandi, Feb 26 2020

Maple

a:= n-> parse(cat($44..44+n)):
seq(a(n), n=0..14);  # Alois P. Heinz, Feb 24 2020

Mathematica

Nest[Append[#, 10^IntegerLength[#2]*#1[[-1]] + #2 ] & @@ {#, 44 + Length@ #} &, {44}, 13] (* Michael De Vlieger, Feb 24 2020 *)
Table[FromDigits[Flatten[IntegerDigits/@Range[44,44+n]]],{n,0,20}] (* Harvey P. Dale, Jul 19 2024 *)