A155985 -id:A155985 - cp's OEIS frontend

A159194 a(n) = sqrt(A155985(n)).

1, 4, 8, 2, 7, 3, 31, 11, 12, 21, 13, 95, 23, 96, 25, 24, 26, 78, 22, 64, 79, 14, 81, 32, 65, 71, 33, 97, 98, 66, 82, 67, 99, 34, 83, 301, 35, 72, 68, 69, 36, 245, 73, 302, 201, 37, 303, 304, 246, 247, 305, 74, 248, 202, 203, 306, 249, 38, 204, 251, 39, 41, 42, 205, 75, 76

Offset: 1

Zak Seidov, Apr 05 2009

nonn

1. Sequence is infinite.
2. First absent numbers are:
5, 6, 9, 10, 15, 16, 17, 18, 19, 20, 27, 28, 29, 30, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 70, 80, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 100.

A155985

A333663 a(1) = 1, then a(n) is the smallest square not occurring earlier and starting with the last nonzero digit of a(n-1).

Original entry on oeis.org

1, 16, 64, 4, 49, 9, 900, 961, 100, 121, 144, 400, 441, 169, 9025, 529, 9216, 625, 576, 676, 6084, 484, 4096, 6241, 196, 6400, 4225, 5041, 1024, 4356, 6561, 1089, 9409, 9604, 4489, 9801, 1156, 6724, 4624, 4761, 1225, 5184, 4900, 90000, 90601, 1296, 6889, 91204

Offset: 1

Bernard Schott, Sep 03 2020

Every term begins with 1, 4, 5, 6 or 9.

			The smallest square not yet in the data that begins with 1 is 16, hence a(2) = 16.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A155985 (variant).

Subsequences of squares with initial digit k: A045784 (k=1), A045787 (k=4), A045788 (k=5), A045789 (k=6), A045793 (k=9).

Nest[Block[{a = #, k = 1, d = Mod[#[[-1]]/10^IntegerExponent[#[[-1]] ], 10]}, While[Nand[FreeQ[a, #], d == Floor[#/10^(IntegerLength[#] - 1)] ] &[k^2], k++]; Append[a, k^2]] &, {1}, 47] (* Michael De Vlieger, Sep 11 2020 *)

nxt(va, d) = {my(k=1); while ((digits(k^2)[1]!=d) || #select(x->(x==k^2), va), k++); k^2;}
lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = nxt(va, digits(fromdigits(Vecrev(digits(va[n-1]))))[1]);); va;} \\ Michel Marcus, Sep 04 2020

More terms from Michel Marcus, Sep 04 2020

A155986 a(1), then a(n) = smallest cube not occurring earlier, not ending with zero and starting with the last digit of a(n-1).

Original entry on oeis.org

1, 125, 512, 27, 729, 9261, 1331, 1728, 8, 85184, 4096, 64, 4913, 343, 3375, 5832, 216, 6859, 91125, 50653, 32768, 804357, 74088, 830584, 42875, 54872, 2197, 79507, 704969, 97336, 68921, 10648, 857375, 59319, 912673, 35937, 753571, 12167, 778688

Offset: 1

Zak Seidov, Feb 01 2009

Cf. A076653, A155985.

cp's OEIS Frontend

A159194 a(n) = sqrt(A155985(n)).

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A333663 a(1) = 1, then a(n) is the smallest square not occurring earlier and starting with the last nonzero digit of a(n-1).

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A155986 a(1), then a(n) = smallest cube not occurring earlier, not ending with zero and starting with the last digit of a(n-1).

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