A332562 - OEIS

%I #36 Jul 19 2024 14:41:53

%S 44,4445,444546,44454647,4445464748,444546474849,44454647484950,

%T 4445464748495051,444546474849505152,44454647484950515253,

%U 4445464748495051525354,444546474849505152535455,44454647484950515253545556,4445464748495051525354555657

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

%C This is an instance of a sequence arising in A332580.

%C 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).

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

%H Robert Israel, <a href="/A332562/b332562.txt">Table of n, a(n) for n = 0..350</a>

%H J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000 [math.NT], April 2020.

%p a:= n-> parse(cat($44..44+n)):

%p seq(a(n), n=0..14);  # _Alois P. Heinz_, Feb 24 2020

%t Nest[Append[#, 10^IntegerLength[#2]*#1[[-1]] + #2 ] & @@ {#, 44 + Length@ #} &, {44}, 13] (* _Michael De Vlieger_, Feb 24 2020 *)

%t Table[FromDigits[Flatten[IntegerDigits/@Range[44,44+n]]],{n,0,20}] (* _Harvey P. Dale_, Jul 19 2024 *)

%o (Magma) [Seqint(Reverse(&cat[Reverse(Intseq(k)): k in [44..n]])): n in [44..60]]; // _Vincenzo Librandi_, Feb 26 2020

%Y Cf. A332580.

%K nonn,base

%O 0,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 24 2020