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%I #29 May 26 2018 22:11:54
%S 1,14,2,74,21,3,147,120,13,4,174,121,37,14,5,471,1120,137,74,25,6,
%T 1135,1121,731,147,125,16,7,1531,14121,1135,174,521,67,17,8,5131,
%U 21114,1531,471,1125,76,77,18,9,13145,21174,5131,1135,1521,167,177,78,19,10
%N A(n, k) is the smallest number x > A(n, k-1) such that every letter, with repetition, that occurs in the English name of A(n, k-1) also occurs in the English name of x, with A(n, 1) = n; square array, read by antidiagonals downwards.
%H <a href="/index/Na">Index entries for sequences related to names of numbers</a>
%F A(n, 1) = n. For k > 1, A(n, k) = A303475(A(n, k-1)).
%e Array starts
%e 1, 14, 74, 147, 174, 471, 1135, 1531, 5131, 13145, ...
%e 2, 21, 120, 121, 1120, 1121, 14121, 21114, 21174, 21471, ...
%e 3, 13, 37, 137, 731, 1135, 1531, 5131, 13145, 13541, ...
%e 4, 14, 74, 147, 174, 471, 1135, 1531, 5131, 13145, ...
%e 5, 25, 125, 521, 1125, 1521, 5121, 11249, 11294, 11492, ...
%e 6, 16, 67, 76, 167, 176, 671, 761, 1165, 1561, ...
%e 7, 17, 77, 177, 771, 1175, 1571, 5171, 14175, 14571, ...
%e 8, 18, 78, 178, 871, 1178, 1871, 8171, 14178, 14871, ...
%e 9, 19, 79, 97, 137, 731, 1135, 1531, 5131, 13145, ...
%e ...
%e Initial terms of row n=1 illustrated in detail, with dots denoting places where new letters are inserted:
%e one -> .o...e.n -> fourteen
%e fourteen -> .e.ent.four -> seventyfour
%e seventyfour -> one.u..re.f..tys.v.. -> onehundredfortyseven
%e onehundredfortyseven -> onehundredseventyfo.r -> onehundredseventyfour
%o (PARI) T(n, k) = if (k == 1, n, a303475(T(n, k-1)));
%o tabl(nn) = for (n=1, nn, for (k=1, nn, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Apr 24 2018
%Y Cf. A303475.
%K nonn,word,tabl
%O 1,2
%A _Felix Fröhlich_, Apr 22 2018