[seqfan] Three infinite sequences

[Eric Angelini]

Hello SeqFans,

S gathers the integers that have a digit
which is the sum of all other digits (of the said integer):

S= 11,22,33,44,55,66,77,88,99,101,110,
112,121,123,132,134,143,145,154,156,
165,167,176,178,187,189,198,211,...
S is infinite: you can write as many zeroes
as you want after 101...
------------
P gathers the integers that have a digit
which is the product of all other digits (of the said integer):

P=11,22,33,44,55,66,77,88,99,100,111,
122,133,144,155,166,177,188,199,200,
212,221,224,242,300,313,331,400,414,...
P is infinite: you can write as many "1"s
after 11...
------------
INT is the intersection between S and P:

INT=11,22,33,44,55,66,77,88,99,224,
242,422,1001,1010,1100,1236,1263,1326,1362,1623,
1632,2136,2163,2316,2361,2613,2631,...

INT is infinite: you can write as many
zeroes as you want after 1001...

Best,
É.