A076653 -id:A076653 - cp's OEIS frontend

A076654 Smallest natural number not a multiple of 10, not occurring earlier and starting with the end of the previous term.

1, 11, 12, 2, 21, 13, 3, 31, 14, 4, 41, 15, 5, 51, 16, 6, 61, 17, 7, 71, 18, 8, 81, 19, 9, 91, 101, 102, 22, 23, 32, 24, 42, 25, 52, 26, 62, 27, 72, 28, 82, 29, 92, 201, 103, 33, 34, 43, 35, 53, 36, 63, 37, 73, 38, 83, 39, 93, 301, 104, 44, 45, 54, 46, 64, 47, 74, 48, 84, 49, 94

Offset: 1

Amarnath Murthy, Oct 28 2002

Reinhard Zumkeller, Table of n, a(n) for n = 1..8936, all terms < 10000

Cf. A076652, A076653.

Cf. A000030, A010879, A067251.

import Data.List (delete)
a076654 n = a076654_list !! (n-1)
a076654_list = f a067251_list 1 where
  f xs z = g xs where
    g (y:ys) = if a000030 y == mod z 10 then y : f (delete y xs) y else g ys
-- Reinhard Zumkeller, Aug 15 2015

startsWith := proc(n,dig) local nshft ; nshft := n ; while nshft >= 10 do nshft := floor(nshft/10) ; od ; if dig = nshft then RETURN(true) ; else RETURN(false) ; fi ; end: A076654 := proc(nmax) local candid,a; a := [1] ; while nops(a) < nmax do candid := 2 ; while not startsWith(candid,op(-1,a) mod 10) or candid mod 10 = 0 or candid in a do candid := candid+1 ; od ; a := [op(a),candid] ; od ; RETURN(a) ; end: a := A076654(200) : for n from 1 to nops(a) do printf("%d,",op(n,a)) ; od ; # R. J. Mathar, Nov 12 2006

A000030(a(n+1)) = A010879(a(n)). - Reinhard Zumkeller, Aug 15 2015

More terms from R. J. Mathar, Nov 12 2006

A155985 a(1)=1, then a(n) is the smallest square not occurring earlier, not ending with zero and starting with the last digit of a(n-1).

Original entry on oeis.org

1, 16, 64, 4, 49, 9, 961, 121, 144, 441, 169, 9025, 529, 9216, 625, 576, 676, 6084, 484, 4096, 6241, 196, 6561, 1024, 4225, 5041, 1089, 9409, 9604, 4356, 6724, 4489, 9801, 1156, 6889, 90601, 1225, 5184, 4624, 4761, 1296, 60025, 5329, 91204, 40401, 1369

Offset: 1

Zak Seidov, Feb 01 2009

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

Cf. A076653 (similar, with primes), A155986.

nxt(va, d) = {my(k=1); while ((digits(k^2)[1]!=d) || !(k%10) || #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, Vecrev(digits(va[n-1]))[1]);); va;} \\ Michel Marcus, Sep 04 2020

\\ See Corneth link. David A. Corneth, Sep 05 2020

Name edited by Michel Marcus, Sep 04 2020

A076652 Smallest composite number not divisible by 10, not occurring earlier and starting with the end of the previous term.

Original entry on oeis.org

4, 42, 21, 12, 22, 24, 44, 45, 51, 14, 46, 6, 62, 25, 52, 26, 63, 32, 27, 72, 28, 8, 81, 15, 54, 48, 82, 201, 16, 64, 49, 9, 91, 18, 84, 402, 202, 203, 33, 34, 403, 35, 55, 56, 65, 57, 74, 404, 405, 58, 85, 501, 102, 204, 406, 66, 68, 86, 69, 92, 205, 502, 206, 602, 207, 75

Offset: 1

Amarnath Murthy, Oct 28 2002

Cf. A076653, A076654.

More terms from Matthew Ohlsen (mjo178(AT)psu.edu), Feb 26 2006

More terms from Max Alekseyev, Sep 14 2009

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.

A262254 a(1) = 11; for n>1, a(n) is the smallest prime that starts with the least significant digit of the previous term and has not occurred earlier.

Original entry on oeis.org

11, 13, 31, 17, 71, 19, 97, 73, 37, 79, 907, 701, 101, 103, 307, 709, 911, 107, 719, 919, 929, 937, 727, 733, 311, 109, 941, 113, 313, 317, 739, 947, 743, 331, 127, 751, 131, 137, 757, 761, 139, 953, 337, 769, 967, 773, 347, 787, 797, 7001, 149, 971, 151, 157, 7013, 349, 977, 7019, 983

Offset: 1

Maghraoui Abdelkader, Sep 16 2015

This sequence is different from A089755, as this one does not include single-digit primes.
This sequence is different from A089755, for which a(n+1) uses all the digit of a(n) except the most-significant digit of a(n).
In this sequence, a(n+1) uses only the least-significant digit of a(n).

			a(3) = 31 where the most significant digit of 31 is 3, which is the least significant digit of a(2) = 13.

Maghraoui Abdelkader, Table of n, a(n) for n = 1..200

Cf. A076653, A082238, A089755, A107809, A180022.

f[s_List] := Block[{lsd = Mod[s[[-1]], 10], p = 3}, While[ IntegerDigits[p][[1]] != lsd || MemberQ[s, p], p = NextPrime@ p]; Append[s, p]]; s = {11}; s = Nest[f, s, 70] (* Robert G. Wilson v, Sep 16 2015 *)

msd(n)=(n\10^(#Str(n)-1)); l1=1;l3=1;l7=1;l9=1; q=1; lsd(n)=n%10;
t1 = vector(200); i=1;forprime(n=11,10000, if( digits(n)[1]==1,t1[i]=n; i=i+1 ; )) ;
t3 = vector(130); i=1;forprime(n=31,3900 ,  if( digits(n)[1]==3,t3[i]=n; i=i+1 ; ));
t7 = vector(130); i=1;forprime(n=71,70000, if( digits(n)[1]==7,t7[i]=n; i=i+1 ; )) ;
t9 = vector(130); i=1;forprime(n=97,90000, if( digits(n)[1]==9,t9[i]=n; i=i+1 ; )) ;lsd(n)=n%10;
t = vector(200);
findnextnumber(m) =
{if(lsd(m)==1, l1=t1[i1] ; i1=i1+1;return(l1);); if(lsd(m)==3, l3=t3[i3];  i3=i3+1 ; return(l3););
if(lsd(m)==7, l7=t7[i7] ; i7=i7+1;return(l7);); if(lsd(m)==9, l9=t9[i9];  i9=i9+1;return(l9);); }
i1=1;  i3=1;  i7=1;  i9=1;  j=1;s=11;   for(n=1,200,   p=findnextnumber(s) ; t[j]=p; s=p;j++);for(i=1,200, print1(t[i],", ") )

A262702 Lexicographically earliest sequence of distinct prime numbers such that the decimal representations of two consecutive terms overlap.

Original entry on oeis.org

2, 23, 3, 13, 11, 17, 7, 37, 43, 31, 19, 41, 101, 61, 103, 71, 47, 73, 67, 79, 97, 29, 229, 293, 307, 53, 5, 59, 359, 83, 283, 311, 107, 131, 109, 151, 113, 137, 181, 127, 191, 139, 211, 149, 241, 157, 251, 163, 271, 167, 281, 173, 313, 193, 317, 179, 331, 197

Offset: 1

Paul Tek, Sep 27 2015

Two terms are said to overlap:
- if the decimal representation of one term is contained in the decimal representation of the other term (for example, 23 and 3 overlap),
- or if, for some k>0, the first k decimal digits (without leading zero) of one term correspond to the k last decimal digits of the other term (for example, 317 and 179 overlap).
This is a variation of A262323 around the prime numbers.
Is this a permutation of the prime numbers?

			The first terms of the sequence are:
+----+--------+
| n  | a(n)   |
+----+--------+
|  1 |  2     |
|  2 |  23    |
|  3 |   3    |
|  4 |  13    |
|  5 | 11     |
|  6 |  17    |
|  7 |   7    |
|  8 |  37    |
|  9 | 43     |
| 10 |  31    |
| 11 |   19   |
| 12 |  41    |
| 13 |   101  |
| 14 |  61    |
| 15 |   103  |
| 16 |  71    |
| 17 | 47     |
| 18 |  73    |
| 19 | 67     |
| 20 |  79    |
| 21 |   97   |
| 22 |  29    |
| 23 | 229    |
| 24 |  293   |
| 25 |    307 |
+----+--------+

Paul Tek, Table of n, a(n) for n = 1..35526
Paul Tek, PERL program for this sequence

Cf. A076653, A262323.

Perl
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See Links section.
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cp's OEIS Frontend

A076654 Smallest natural number not a multiple of 10, not occurring earlier and starting with the end of the previous term.

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A155985 a(1)=1, then a(n) is the smallest square not occurring earlier, not ending with zero and starting with the last digit of a(n-1).

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A076652 Smallest composite number not divisible by 10, not occurring earlier and starting with the end of the previous term.

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Author

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Crossrefs

Extensions

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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A262254 a(1) = 11; for n>1, a(n) is the smallest prime that starts with the least significant digit of the previous term and has not occurred earlier.

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Mathematica

PARI

A262702 Lexicographically earliest sequence of distinct prime numbers such that the decimal representations of two consecutive terms overlap.

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Author

Keywords

Comments

Examples

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Crossrefs

Programs

Perl