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%I #44 Jun 29 2023 12:38:50
%S 2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N a(1) = 2; for n > 1, a(n) = 3.
%C a(n) = number of neighboring natural numbers of n (e.g., n, n-1, n+1).
%C a(n) = A158799(n) for n >= 1. - _Jaroslav Krizek_, Nov 18 2009
%C Also decimal expansion of 7/3. - _Natan Arie Consigli_, May 02 2015
%C Decimal expansion of Sum_{i>=0} (4/7)^i. - _Bruno Berselli_, Aug 23 2017
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F a(n) = 1[0]1[1]1...1[n-1]1[n]1, where [0] is zeration or successor (y[0]x = x+1), [1] addition, [2] multiplication, [3] exponentiation, [4] repeated exponentiation, etc. - _Natan Arie Consigli_, May 02 2015
%F G.f.: x*(2+x)/(1-x). - _Robert Israel_, May 07 2015
%e a(4) = 1[0]1[1]1[2]1[3]1[4]1 = '1+1*1^1^^1 = 3. - _Natan Arie Consigli_, May 02 2015
%t {2}~Join~Table[3, {120}] (* _Michael De Vlieger_, May 05 2015 *)
%t PadRight[{2},120,3] (* _Harvey P. Dale_, Aug 12 2021 *)
%o (PARI) A157532(n)=2+(n>1) \\ _M. F. Hasler_, Jul 30 2015
%Y Cf. A254310 (3[0]3[1]...[n]3), A254225 (2[0]2[1]...[n]2).
%Y Except for initial terms, the same as A156752 and A165020. - _M. F. Hasler_, Jul 30 2015
%K nonn,easy,less,cons
%O 1,1
%A _Jaroslav Krizek_, Mar 02 2009
%E More threes from _R. J. Mathar_, Mar 14 2009; truncated to three lines by _M. F. Hasler_, Jul 30 2015
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