A303380 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.

1, 14, 2, 74, 21, 3, 147, 120, 13, 4, 174, 121, 37, 14, 5, 471, 1120, 137, 74, 25, 6, 1135, 1121, 731, 147, 125, 16, 7, 1531, 14121, 1135, 174, 521, 67, 17, 8, 5131, 21114, 1531, 471, 1125, 76, 77, 18, 9, 13145, 21174, 5131, 1135, 1521, 167, 177, 78, 19, 10

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Index entries for sequences related to names of numbers

Formula

A(n, 1) = n. For k > 1, A(n, k) = A303475(A(n, k-1)).

Example

Array starts
1, 14,  74, 147,  174,  471,  1135,  1531,  5131, 13145, ...
2, 21, 120, 121, 1120, 1121, 14121, 21114, 21174, 21471, ...
3, 13,  37, 137,  731, 1135,  1531,  5131, 13145, 13541, ...
4, 14,  74, 147,  174,  471,  1135,  1531,  5131, 13145, ...
5, 25, 125, 521, 1125, 1521,  5121, 11249, 11294, 11492, ...
6, 16,  67,  76,  167,  176,   671,   761,  1165,  1561, ...
7, 17,  77, 177,  771, 1175,  1571,  5171, 14175, 14571, ...
8, 18,  78, 178,  871, 1178,  1871,  8171, 14178, 14871, ...
9, 19,  79,  97,  137,  731,  1135,  1531,  5131, 13145, ...
...
Initial terms of row n=1 illustrated in detail, with dots denoting places where new letters are inserted:
one -> .o...e.n -> fourteen
fourteen -> .e.ent.four -> seventyfour
seventyfour -> one.u..re.f..tys.v.. -> onehundredfortyseven
onehundredfortyseven -> onehundredseventyfo.r -> onehundredseventyfour

Prog

(PARI) T(n, k) = if (k == 1, n, a303475(T(n, k-1)));
tabl(nn) = for (n=1, nn, for (k=1, nn, print1(T(n, k), ", ")); print); \\ Michel Marcus, Apr 24 2018

Crossrefs

Cf. A303475.

Sequence in context: A040195 A335701 A377037 * A242061 A040189 A088576

Adjacent sequences: A303377 A303378 A303379 * A303381 A303382 A303383

Keyword

nonn,word,tabl

Author

Felix Fröhlich, Apr 22 2018

Status

approved