A100787 -id:A100787 - cp's OEIS frontend

A100880 First differences of A100787.

1, 2, 4, 8, 1, 6, 1, 7, 2, 3, 2, 4, 3, 1, 3, 3, 3, 6, 3, 8, 4, 2, 4, 5, 4, 6, 4, 9, 5, 2, 5, 5, 6, 1, 6, 4, 7, 2, 7, 6, 7, 8, 8, 2, 8, 7, 9, 1, 9, 7, 1, 0, 1, 1, 1, 0, 1, 1, 5, 1, 1, 7, 1, 2, 2, 1, 2, 7, 1, 3, 3, 1, 3, 4, 1, 4, 0, 1, 4, 4, 1, 5, 1, 1, 5, 3, 1, 6, 0, 1, 6, 6, 1, 7, 3, 1, 8, 1, 1

Offset: 1

N. J. A. Sloane, Jan 11 2005

nonn

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

A211206 Least number which reaches n under the operation introduced in A100787: first differences are the digits of the sequence.

Original entry on oeis.org

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 3, 5, 3, 1, 1, 5, 3, 3, 11, 5, 1, 1, 3, 3, 5, 5, 19, 13, 1, 3, 1, 5, 7, 1, 7, 1, 7, 5, 5, 1, 13, 3, 1, 1, 11, 9, 1, 5, 3, 1, 3, 11, 1, 9, 20, 13, 3, 7, 1, 3, 5, 1, 5, 9, 3, 5, 9, 3, 11, 1, 7, 3, 11, 1, 5, 1

Offset: 1

Eric Angelini and M. F. Hasler, Feb 04 2013

E. Angelini proposes to call Wilsonize(n) the sequence starting with n and having as first differences the digits of the (concatenated) terms of the sequence. Then this sequence lists the smallest starting value a(n)=k such that n is a term of Wilsonize(k).

E. Angelini, Smallest hitters, SeqFan list, Feb 04 2013

A211206(n)={ for(k=1,n, my(seed=k,d=digits(seed)); while(seed

A339951 Similar to A100787, but alternate with addition and multiplication instead. See Comments section for more information.

Original entry on oeis.org

1, 2, 4, 8, 64, 70, 280, 287, 0, 2, 16, 16, 32, 40, 280, 280, 560, 561, 3366, 3367, 20202, 20205, 40410, 40414, 0, 2, 16, 16, 32, 40, 0, 5, 30, 30, 150, 156, 156, 159, 477, 483, 2898, 2901, 8703, 8709, 60963, 60965, 0, 2, 0, 2, 4, 4, 8, 8, 40, 44, 0, 4, 4, 4

Offset: 0

Jamie Robert Creasey, Dec 24 2020

We start with a(0) as 1, placing an addition sign below the digit. As such, we add 1 to a(0) to receive the next term which is 2. This time, place a multiplication sign below the new digit and double a(1) to receive a(2) which is 4. Place add under the next unused digit and add this to a(2), followed by multiply under the next a(3) and repeat.

Unlike A100787, terms within this sequence are not strictly increasing, as the 8th digit in this sequence is a 0 where we apply multiplication. Also, the differences do not reflect the digits of this sequence, due to alternation with multiplication. The records are 1, 2, 4, 8, 64, 70, 280, 287, 280, 560, 561, 3366 ...

			1, 2, 4, 8, 64, 70, 280, 287, 0, 2, 16, ...
+  *  +  *  +*  +*  +*+  *+*  +  *  +*
To calculate a(5), we add 6 to 64, as the 5th digit is a 6 with the add operator underneath. Thus, a(5) is 70.
To calculate a(8), we multiply 287 by 0, as the 8th digit is a 0 with the multiply operator underneath. Thus, a(8) is 0.

Cf. A100787, A107974, A107975, A107976, A107977.

A107975 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

5, 10, 11, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 27, 28, 33, 34, 40, 41, 49, 50, 59, 61, 63, 65, 68, 70, 77, 79, 87, 90, 93, 96, 100, 104, 104, 108, 109, 113, 122, 127, 127, 132, 141, 147, 148, 154, 157, 163, 168, 174, 182, 189, 189, 196, 203, 210, 219, 227, 234, 243

Offset: 1

Eric Angelini, Jun 12 2005

			5.10.11.11.12.13.14.15.16.18 ... <- sequence
.5..1..0..1..1..1..1..1..2 ... <- first differences are the sequence's digits.

Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

a[1] = 5; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 61}] (* Robert G. Wilson v, Jun 15 2005 *)

Edited and extended by Robert G. Wilson v, Jun 15 2005

A107974 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

3, 6, 12, 13, 15, 16, 19, 20, 25, 26, 32, 33, 42, 44, 44, 46, 51, 53, 59, 62, 64, 67, 70, 74, 76, 80, 84, 88, 92, 96, 102, 107, 108, 113, 116, 121, 130, 136, 138, 144, 148, 154, 161, 168, 168, 175, 179, 186, 192, 200, 200, 208, 212, 220, 228, 237, 239, 248, 254, 255

Offset: 1

Eric Angelini, Jun 12 2005

			3.6.12.13.15.16.19.20.25 ... <- sequence
.3.6..1..2..1..3..1..5 ... <- first differences are the sequence's digits.

Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

a[1] = 3; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 60}] (* Robert G. Wilson v, Jun 15 2005 *)

Edited and extended by Robert G. Wilson v, Jun 15 2005

A107976 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

7, 14, 15, 19, 20, 25, 26, 35, 37, 37, 39, 44, 46, 52, 55, 60, 63, 70, 73, 80, 83, 92, 96, 100, 104, 110, 115, 117, 122, 127, 133, 133, 139, 142, 149, 149, 156, 159, 167, 167, 175, 178, 187, 189, 198, 204, 205, 205, 205, 206, 206, 210, 211, 212, 212, 213, 214

Offset: 1

Eric Angelini, Jun 12 2005

Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

			7.14.15.19.20.25.26.35.37.37... <- sequence
.7..1..4..1..5..1..9..2..0... <- first differences = the sequence's digits

a[1] = 7; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 60}] (* Robert G. Wilson v, Jun 15 2005 *)

Edited and extended by Robert G. Wilson v, Jun 15 2005

A107977 First differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

9, 18, 19, 27, 28, 37, 39, 46, 48, 56, 59, 66, 69, 78, 82, 88, 92, 100, 105, 111, 116, 125, 131, 137, 143, 152, 159, 167, 175, 177, 185, 193, 202, 204, 205, 205, 205, 206, 206, 211, 212, 213, 214, 215, 216, 222, 223, 225, 230, 231, 234, 235, 236, 239, 246, 247

Offset: 1

Eric Angelini, Jun 12 2005

			9.18.19.27.28.37.39.46.48.56 ... <- sequence
.9..1..8..1..9..2..7..2..8 ... <- first differences are the sequence's digits.

Cf. A100787, A107974, A107975, A107976, A107977 for "seeds" 1, 3, 5, 7 and 9.

a[1] = 9; a[n_] := a[n] = a[n - 1] + Flatten[ Table[ IntegerDigits[ a[i]], {i, n - 1}]][[n - 1]]; Table[ a[n], {n, 56}] (* Robert G. Wilson v, Jun 15 2005 *)

Edited and extended by Robert G. Wilson v, Jun 15 2005

A077321 Rearrange primes so as to form a triangle in which n-th row contains the n smallest primes == 1 (mod n) which have not occurred earlier.

Original entry on oeis.org

2, 3, 5, 7, 13, 19, 17, 29, 37, 41, 11, 31, 61, 71, 101, 43, 67, 73, 79, 97, 103, 113, 127, 197, 211, 239, 281, 337, 89, 137, 193, 233, 241, 257, 313, 353, 109, 163, 181, 199, 271, 307, 379, 397, 433, 131, 151, 191, 251, 311, 331, 401, 421, 431, 461, 23, 419, 463, 617

Offset: 1

Amarnath Murthy, Nov 04 2002, Nov 30 2004

			Triangle begins:
2
3 5
7 13 19
17 29 37 41
11 31 61 71 101
...

Ivan Neretin, Table of n, a(n) for n = 1..5050

Cf. A077322, A077323, A077324, A077325.

Cf. A100787, A100788, A100789, A100790.

A077321 := proc(nmax) local n,a,i,p; a := []; n :=1; while nops(a) < nmax do for i from 1 to n do p := 2; while ( p in a ) or (p-1) mod n <> 0 do p := nextprime(p); od; a := [op(a),p]; od; n := n+1; od; RETURN(a); end: A077321(100); # R. J. Mathar, Feb 03 2007

A077321[nmax_] := Module[{n = 1, a = {}, i, p}, While[ Length[a] < nmax, For[i = 1, i <= n, i++,  p = 2; While[ MemberQ[a, p] || Mod[p - 1, n] != 0, p = NextPrime[p]]; a = Append[a, p]]; n = n + 1]; Return[a]];
A077321[100] (* Jean-François Alcover, May 30 2023, after R. J. Mathar *)

More terms from Ray Chandler, Dec 10 2004

Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar

A108787 Binary numbers such that the first differences give the same sequence written as a string of individual digits.

Original entry on oeis.org

1, 10, 11, 11, 100, 101, 110, 111, 1000, 1000, 1000, 1001, 1001, 1010, 1011, 1100, 1100, 1101, 1110, 1111, 10000, 10000, 10000, 10000, 10001, 10001, 10001, 10001, 10010, 10010, 10010, 10010, 10011, 10011, 10011, 10100, 10101, 10101

Offset: 1

Philippe Deléham, Jul 09 2005

			1, 10, 11, 11, 100, 101, 110, 111, 1000, 1000, 1001, 1001, ... <- sequence (base 2)
..1..1..0..1..1..1..1..1..0..0..1..0... <- first difference are the sequence's digits.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A108788, A108789, A108790.

Cf. A100787 for a similar sequence in decimal.

A[1]:= 1: B:= 1: S:= "1":
for n from 2 to 100 do
  B:= B + parse(S[n-1]);
  A[n]:= convert(B,binary);
  S:= cat(S,A[n]);
od:
seq(A[i],i=1..100); # Robert Israel, Jun 11 2019

A334336 Write under each comma the absolute difference of the two digits framing the said comma; the successive results reproduce, digit by digit, the sequence itself. This is the lexicographically earliest permutation of the positive integers with this property.

Original entry on oeis.org

1, 2, 4, 80, 8, 81, 9, 10, 100, 90, 11, 12, 3, 31, 110, 91, 13, 40, 14, 5, 7, 41, 42, 30, 15, 6, 60, 92, 32, 33, 61, 51, 16, 70, 43, 82, 93, 71, 20, 44, 62, 52, 21, 22, 72, 83, 94, 400, 95, 73, 63, 50, 34, 77, 17, 84, 96, 74, 53, 98, 18, 85, 97, 49, 19, 700, 99, 68, 101, 23, 54, 45, 900

Offset: 1

Eric Angelini and Carole Dubois, Apr 23 2020

			Compare the start of the sequence and the absolute comma-differences:
Seq = 1, 2, 4, 80, 8, 81, 9, 10, 100, 90, 11, 12, 3, 31, 110, 91, ...
Dif = .1..2..4...8..0...8..8...1....9...1...0...1..0...0....9...
We see that the digits of the second line reproduce the digits' succession of the first line.

Carole Dubois, Table of n, a(n) for n = 1..5000
Eric Angelini, Comma differences, message to the SeqFan mailing list, March 22 2020.

Cf. A100787.

cp's OEIS Frontend

A100880 First differences of A100787.

Views

Author

Keywords

References

A211206 Least number which reaches n under the operation introduced in A100787: first differences are the digits of the sequence.

Views

Author

Keywords

Comments

Links

Programs

PARI

A339951 Similar to A100787, but alternate with addition and multiplication instead. See Comments section for more information.

Views

Author

Keywords

Comments

Examples

Crossrefs

A107975 First differences give the same sequence written as a string of individual digits.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A107974 First differences give the same sequence written as a string of individual digits.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A107976 First differences give the same sequence written as a string of individual digits.

Views

Author

Keywords

Comments

Examples

Programs

Mathematica

Extensions

A107977 First differences give the same sequence written as a string of individual digits.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A077321 Rearrange primes so as to form a triangle in which n-th row contains the n smallest primes == 1 (mod n) which have not occurred earlier.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A108787 Binary numbers such that the first differences give the same sequence written as a string of individual digits.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

A334336 Write under each comma the absolute difference of the two digits framing the said comma; the successive results reproduce, digit by digit, the sequence itself. This is the lexicographically earliest permutation of the positive integers with this property.

Views

Author