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Repunits concatenated with A000422, where A000422 is the concatenation of numbers from n down to 1.
2

%I #16 Aug 23 2022 18:34:32

%S 11,1121,111321,11114321,1111154321,111111654321,11111117654321,

%T 1111111187654321,111111111987654321,111111111110987654321,

%U 111111111111110987654321,111111111111121110987654321

%N Repunits concatenated with A000422, where A000422 is the concatenation of numbers from n down to 1.

%C See A078569 for the primes arising in this sequence.

%H Harvey P. Dale, <a href="/A078568/b078568.txt">Table of n, a(n) for n = 1..277</a>

%t a[n_Integer] := Block[{repUn = Array[Array[1 &, #] &, {n}], nTo1 = Range[ Range@n, 1, -1]}, ToExpression/@ StringJoin/@ Map[ToString, Flatten/@ Thread@{repUn, nTo1}, {2}]]; a[100] (* or *)

%t a[n_Integer] := FromDigits /@ StringJoin /@ Table[ Join[ PadLeft[{}, i, "1"], ToString /@ Range[i, 1, -1]], {i, n}]; a[100] (* _Mikk Heidemaa_, May 03 2021 *)

%t Table[FromDigits[Join[PadRight[{},n,1],Flatten[IntegerDigits/@Range[n,1,-1]]]],{n,20}] (* _Harvey P. Dale_, Aug 23 2022 *)

%Y Cf. A002275, A000422, A078569.

%K base,nonn

%O 1,1

%A _Jason Earls_, Nov 29 2002