This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Illustration using the member of this sequence - number 56789765: . . . . 9 . . . . . . 8 . . . . . . 7 . . 7 . . . 6 . . . . 6 . 5 . . . . . . 5
Illustration using a term of this sequence, 4566664: . . 6 6 6 6 . . 5 . . . . . 4 . . . . . 4
nonz[v_] := Select[v,#!=0 &]; hillQ[n_] := Module[{d=IntegerDigits[n]}, If[d[[1]] != d[[-1]], Return[False]]; MemberQ[{{},{0},{-2}}, nonz@ Differences@ Sign@ nonz@ Differences@d]]; Select[Range[1000], hillQ] (* Amiram Eldar, Dec 19 2018 *)
a(6)=121 is in the sequence because 121 is a nonprime number A018252 and 121 is also a Giza number A134810. The last six terms of this finite sequence are a(32) = 1234567654321 a(33) = 2345678765432 a(34) = 3456789876543 a(35) = 123456787654321 a(36) = 234567898765432 a(37) = 12345678987654321 Illustration of a(37) as a Giza nonprime: . . . . . . . . 9 . . . . . . . . . . . . . . . 8 . 8 . . . . . . . . . . . . . 7 . . . 7 . . . . . . . . . . . 6 . . . . . 6 . . . . . . . . . 5 . . . . . . . 5 . . . . . . . 4 . . . . . . . . . 4 . . . . . 3 . . . . . . . . . . . 3 . . . 2 . . . . . . . . . . . . . 2 . 1 . . . . . . . . . . . . . . . 1
Select[Union[FromDigits/@Select[Flatten[Table[Table[Join[Range[i,i+n], Reverse[ Most[ Range[ i,i+n]]]],{n,0,9}],{i,9}],1],Max[#]<10&]], !PrimeQ[#]&] (* Harvey P. Dale, Aug 23 2011 *)
For n = 0, 10^0 = 1, there is a single A343524 term less than 1: 0. For n = 2, 10^2 = 100, there are 19 A343524 terms less than 100: 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99. Examples of A343524 terms less than 100000: 1661, 28982.
a(n)=sum(k=1, min(n,18)+1, binomial(9,k\2)) \\ Andrew Howroyd, Jan 22 2024
from math import comb
def a(n):
if n > 18: return 1023
return 1+sum(comb(9, (digits+1)//2) for digits in range(1, n+1))
print([a(n) for n in range(47)]) # Michael S. Branicky, Jan 22 2024
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