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A281253 Alternately concatenate the decimal digits from front to back 1...n such that n is always to the right.

%I A281253 #13 May 22 2025 10:21:45
%S A281253 1,12,213,3124,42135,531246,6421357,75312468,864213579,97531246810,
%T A281253 1086421357911,119753124681012,12108642135791113,1311975312468101214,
%U A281253 141210864213579111315,15131197531246810121416,1614121086421357911131517
%N A281253 Alternately concatenate the decimal digits from front to back 1...n such that n is always to the right.
%C A281253 a(n) is prime for n: 121, 1399 and no others < 3000.
%H A281253 Indranil Ghosh, <a href="/A281253/b281253.txt">Table of n, a(n) for n = 1..340</a>
%e A281253 a(13) = 12108642135791113.
%p A281253 b:= proc(n) b(n):= `if`(n=1, 1, parse(cat(n, a(n-1)))) end:
%p A281253 a:= proc(n) a(n):= `if`(n=1, 1, parse(cat(b(n-1), n))) end:
%p A281253 seq(a(n), n=1..20);  # _Alois P. Heinz_, Jan 18 2017
%t A281253 f[n_] := Fold[ If[ Mod[n +#2, 2] == 0, #1, #2]*10^IntegerLength@ If[ Mod[n +#2, 2] == 0, #2, #1] +If[ Mod[n +#2, 2] == 0, #2, #1] &, 0, Range@ n]; Array[f, 17]
%o A281253 (Python)
%o A281253 def a(n):
%o A281253     if n==1:
%o A281253         return ["1"]
%o A281253     return a(n-1)[::-1]+[str(n)]
%o A281253 def A281253(n):
%o A281253     return "".join(a(n)) # _Indranil Ghosh_, Jan 27 2017
%Y A281253 Cf. A007908, A138957, A000422, A138793, A281254.
%K A281253 nonn,base,easy
%O A281253 1,2
%A A281253 _Robert G. Wilson v_, Jan 18 2017