A369132 -id:A369132 - cp's OEIS frontend

A369092 Numbers which are a substring of their own "Look and Say" description (cf. A045918).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 31, 41, 51, 61, 71, 81, 91, 101, 110, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 141, 151, 161, 171, 181, 191, 221, 322, 422, 522, 622, 722, 822, 922, 1022, 1101, 1121, 1131, 1141, 1151, 1161, 1171, 1181, 1191

Offset: 1

Scott R. Shannon, Jan 13 2024

It is likely the 171 terms of the attached bfile, with a(171) = 22119221, forms the complete list of such numbers, although this is unknown.

			1 is a term as A045918(1) = 10, which contains "1" as a substring.
101 is a term as A045918(101) = 111011, which contains "101" as a substring.
22119221 is a term as A045918(22119221) = 2221192211, which contains "22119221" as a substring. It is likely this is the last possible term.

Scott R. Shannon, Table of n, a(n) for n = 1..171

Cf. A369132 (description is a substring of the number), A005150, A045918.

A379453 Numbers that decrease when they are replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.

Original entry on oeis.org

49, 64, 81, 125, 128, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 961, 1024, 1250, 1331, 1369, 1458, 1681, 1715, 1849, 1875, 2048, 2187, 2197, 2209, 2401, 2500, 2809, 2916, 3087, 3125, 3375, 3481, 3721, 4096, 4374, 4489, 4802, 4913, 5000, 5041, 5329, 5488, 5625, 5832, 6075, 6125, 6241, 6250, 6561, 6859, 6889, 7203, 7776, 7921, 8000, 8192, 8575, 8748

Offset: 1

Scott R. Shannon, Dec 23 2024

			49 is a term as 49 = 7^2 which becomes 27 when replaced by the "Look and Say" description of its prime factors, and 27 is smaller than 49.

Scott R. Shannon, Table of n, a(n) for n = 1..5000

Cf. A045918, A379454, A379455, A005150, A367974, A369132, A369092.

Select[Range[8750],#>FromDigits[Flatten[IntegerDigits/@Reverse/@FactorInteger[#]]]&] (* James C. McMahon, Dec 23 2024 *)

A379455 Numbers that decrease two times in succession when they are iteratively replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.

Original entry on oeis.org

1849, 7921, 38809, 79507, 146529, 160801, 200978, 226981, 327697, 654481, 1113032, 1653125, 1731619, 1765376, 2109375, 2588881, 3418927, 3857868, 4182703, 5640625, 6492304, 6553600, 6892100, 7103125, 7845601, 8438707, 9509327, 11039981, 11880448, 12068352, 12106067, 12584111, 13227109, 14895500, 16843208, 17149469, 17372224, 18081075, 18852697, 19523584

Offset: 1

Scott R. Shannon, Dec 23 2024

nonn

			1849 is a term as 1849 = 43^2 which becomes 243 when replaced by the "Look and Say" description of its prime factors, and 243 is smaller than 1849, and 243 = 3^5 which becomes 53 when replaced by the "Look and Say" description of its prime factors, and 53 is smaller than 243.

Scott R. Shannon, Table of n, a(n) for n = 1..568

Cf. A045918, A379453, A379454, A005150, A367974, A369132, A369092.

A379454 Numbers that decrease three times in succession when they are iteratively replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.

Original entry on oeis.org

727974361, 2204693643, 2643690625

Offset: 1

Scott R. Shannon, Dec 23 2024

			2643690625 is a term as 2643690625 = 5^5 * 845981 which becomes 551845981 when replaced by the "Look and Say" description of its prime factors, and 551845981 is smaller than 2643690625, 551845981 = 239^2 * 9661 which becomes 223919661 when replaced by the "Look and Say" description of its prime factors, and 223919661 is smaller than 551845981, and 223919661 = 3 * 7^5 * 4441 which becomes 135714441 when replaced by the "Look and Say" description of its prime factors, and 135714441 is smaller than 223919661.

Cf. A045918, A379453, A379455, A005150, A367974, A369132, A369092.

cp's OEIS Frontend

A369092 Numbers which are a substring of their own "Look and Say" description (cf. A045918).

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A379453 Numbers that decrease when they are replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.

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A379455 Numbers that decrease two times in succession when they are iteratively replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.

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A379454 Numbers that decrease three times in succession when they are iteratively replaced by the "Look and Say" description (cf. A045918) of their prime factors, counted with multiplicity.

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