A120819 -id:A120819 - cp's OEIS frontend

A057137 Concatenate next digit at right hand end (where the next digit after 9 is again 0).

0, 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567890, 12345678901, 123456789012, 1234567890123, 12345678901234, 123456789012345, 1234567890123456, 12345678901234567, 123456789012345678, 1234567890123456789, 12345678901234567890, 123456789012345678901

Offset: 0

Henry Bottomley, Aug 12 2000

Also called the triangle of the gods (see Pickover link).

See A037610 for a general formula. - Hieronymus Fischer, Jan 03 2013

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61.

T. D. Noe and Hieronymus Fischer, Table of n, a(n) for n = 0..200 (terms up to 100 from T. D. Noe)
Clifford Pickover, Triangle of the Gods
Index entries for linear recurrences with constant coefficients, signature (10,0,0,0,0,0,0,0,0,1,-10).

Alternative progression for n >= 10 compared with A007908 and A014824.
Cf. A057138 for reverse. Cf. A010879 (decimal digits).
For primes see A120819.

A057137:=n->floor((137174210/1111111111)*10^n); seq(A057137(n), n=0..20); # Wesley Ivan Hurt, Apr 18 2014

a[n_]:=Floor[137174210/1111111111*10^n]; Array[a,19,0] (* Robert G. Wilson v, Apr 18 2014 *)

A057137(n)=sum(i=1,n,i%10*10^(n-i)) \\ M. F. Hasler, Jan 13 2013

A057137(n)=137174210*10^n\1111111111 \\ M. F. Hasler, Jan 13 2013

def A057137(n): s = '0123456789'; return int((n+1)//10*s + s[:(n+1)%10]) # Ya-Ping Lu, Apr 08 2025

a(n) = 10*(a(n-1)-floor[n/10]) + n = floor[A057139(n)/10^(n-1)].

a(n) = floor((137174210/1111111111)*10^n). - Hieronymus Fischer, Jan 03 2013, corrected by M. F. Hasler, Jan 13 2013

A120821 a(n) consecutive digits ascending beginning with the digit 3 give a prime.

Original entry on oeis.org

1, 179, 529, 62625

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 3 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 3 give a prime." has only one term, 1 which represents the prime 3.
a(5) > 10^5. - Michael S. Branicky, Apr 08 2025

Cf. A006055, A120819, A120820, A120822, A120823, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[2+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

a(4) from Michael S. Branicky, Apr 03 2025

A120822 a(n) consecutive digits ascending beginning with the digit 4 give a prime.

Original entry on oeis.org

4, 8, 194

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 4; after 9 comes 0.

a(4) > 10^5. - Michael S. Branicky, Apr 08 2025

			8 is a term since 45678901 is a prime.

Cf. A006055, A120829, A120819, A120820, A120821, A120823, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[3+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

A120820 a(n) consecutive digits ascending beginning with the digit 2 give a prime.

Original entry on oeis.org

1, 2, 8, 82, 118, 158, 2122, 2242, 2388

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 2 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 2 give a prime" has only one term, 1 which represents the prime 2.
a(10) > 10^5. - Michael S. Branicky, Apr 10 2025

			8 is a term since 23456789 is a prime.

Cf. A006055, A120819, A120821, A120822, A120823, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[1+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

A120823 a(n) consecutive digits ascending beginning with the digit 5 give a prime..

Original entry on oeis.org

1, 29, 269, 689

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 5 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 5 give a prime." has only one term, 1 which represents the prime 5.
a(5) > 10^5. - Michael S. Branicky, Apr 08 2025

			29 is a term since the 29-digit number 56789012345678901234567890123 is a prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[4+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 9000}]; lst

A120824 a(n) consecutive digits ascending beginning with the digit 6 give a prime.

Original entry on oeis.org

2, 6, 36, 122, 336, 82812

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 6 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 6 give a prime" has no terms.
a(7) >= 100000. - Michael S. Branicky, Apr 07 2025

			6 is a term since 678901 is a prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[5+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

a(6) from Michael S. Branicky, Apr 05 2025

A120825 a(n) consecutive digits ascending beginning with the digit 7 give a prime.

Original entry on oeis.org

1, 5, 15, 51, 8411

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 7 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 7 give a prime" has only two terms below 6001, namely 1 and 5, which represent the primes 7 and 76543, respectively.
a(6) >= 100000. - Michael S. Branicky, Apr 07 2025

			1 is here because 7 is prime.
5 is here because 78901 is prime.
15 is here because 789012345678901 is a prime.
51 is here because 789012345678901234567890123456789012345678901234567 is prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120824, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[6+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

a(5) from Bert Dobbelaere, Apr 01 2025

A120826 a(n) consecutive digits ascending beginning with the digit 8 give a prime.

Original entry on oeis.org

2, 82, 152, 7066, 84892

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 8 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 8 give a prime" has no terms.
a(6) > 10^5. - Michael S. Branicky, Apr 11 2025

			2 is a term since 89 is a prime.
82 is a term because 8901234567890123456789012345678901234567890123456789012345678901234567890123456789 is a prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120824, A120825, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[7+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

a(4) from Bert Dobbelaere, Apr 01 2025

a(5) from Michael S. Branicky, Apr 03 2025

A120827 a(n) consecutive digits ascending beginning with the digit 9 give a prime.

Original entry on oeis.org

13, 29, 43

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 9 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 9 give a prime" has no terms.
There is no further term up to 26000. - Farideh Firoozbakht, Sep 11 2006
There is no further term up to 150000. - Michael S. Branicky, Apr 22 2025

			13 is a term since 9012345678901 is a prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120824, A120825, A120826.

fQ[n_] := PrimeQ@ FromDigits@ Mod[8+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst
Flatten[Position[Table[FromDigits[PadRight[{},n,{9,0,1,2,3,4,5,6,7,8}]],{n,100}],?PrimeQ]] (* _Harvey P. Dale, Sep 06 2015 *)

A120828 Numbers k such that the concatenation of n successive descending digits (1,0,9,8,7,...) starting with 1 is prime.

Original entry on oeis.org

3, 5, 35, 139, 153, 253, 1053, 2015, 3703, 6933, 8173, 11959

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in descending order beginning with 1 and after 0 comes 9.
Terms must end in 3, 5 or 9. - Michael S. Branicky, May 11 2023
a(13) > 10^5. - Michael S. Branicky, Apr 18 2025

			5 is a term since 10987 is a prime.

Cf. A120804, A120819, A120829.

filter:= proc(n) local i; isprime( add(10^(n-1-i)*(1-i mod 10), i=0..n-1)) end proc:
select(filter, [$1..4000]); # Robert Israel, Mar 08 2023

fQ[n_] := PrimeQ@ FromDigits@ Mod[2-Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 6000}]; lst

Name corrected by Robert Israel, Mar 08 2023

a(10)-a(12) from Michael S. Branicky, May 11 2023

cp's OEIS Frontend

A057137 Concatenate next digit at right hand end (where the next digit after 9 is again 0).

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A120821 a(n) consecutive digits ascending beginning with the digit 3 give a prime.

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A120822 a(n) consecutive digits ascending beginning with the digit 4 give a prime.

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A120820 a(n) consecutive digits ascending beginning with the digit 2 give a prime.

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A120823 a(n) consecutive digits ascending beginning with the digit 5 give a prime..

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A120824 a(n) consecutive digits ascending beginning with the digit 6 give a prime.

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A120825 a(n) consecutive digits ascending beginning with the digit 7 give a prime.

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A120826 a(n) consecutive digits ascending beginning with the digit 8 give a prime.

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