A026474 -id:A026474 - cp's OEIS frontend

A276278 Complement of A026474.

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 79

Offset: 1

Bob Selcoe, Aug 26 2016

Numbers of the form prime(k)^a(n) do not appear in A026477.

Terms are all the positive integers except 1, 2, 4 and numbers of the form 7k+1.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Cf. A026474, A026477.

[n+Ceiling((n+2)/6)+2: n in [0..100]]; // Vincenzo Librandi, Aug 27 2016

3, seq(n + ceil((n+2)/6)+2, n=2..100); # Robert Israel, Sep 09 2016

Join[{3}, LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {5, 6, 7, 9, 10, 11, 12}, 100]] (* Vincenzo Librandi, Aug 27 2016 *)

a(n)=if(n>1, n+(n+7)\6, 2) \\ Charles R Greathouse IV, Aug 27 2016

Vec((3+2*x+x^2+x^3+2*x^4+x^5-2*x^6-x^7)/(1-x-x^6+x^7) + O(x^99)) \\ Altug Alkan, Sep 09 2016

For n>=2, a(n) = n + ceiling((n+2)/6) + 2.
For n>=8, a(n) = a(n-6) + 7.
G.f.: (3+2*x+x^2+x^3+2*x^4+x^5-2*x^6-x^7)/(1-x-x^6+x^7). - Robert Israel, Sep 09 2016

A026477 a(1) = 1, a(2) = 2, a(3) = 3; and for n > 3, a(n) = smallest number > a(n-1) and not of the form a(i)a(j)a(k) for 1 <= i < j < k < n.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 120, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 168, 169, 173, 179, 181, 191, 193, 197, 199, 210, 211, 216, 223

Offset: 1

Clark Kimberling

nonn

From Bob Selcoe, Aug 25 2016: (Start)
Once a term with a given prime signature S (i.e., multiset of prime exponents) appears, then all numbers with the same prime signature follow. So either all or no terms with the same prime signature appear (first conjectured by Charles R Greathouse IV).
Proof:
i. Let S = {i,j,k..,y}, i>=j>=k.. be prime signatures, i.e., numbers of the form (p^i*q^j*r^k..*z^y) where {p,q,r,..,z} are distinct primes; denote S = {} as the signature for p^0 = 1.
ii. By definition, 1 and all primes p appear in the sequence; so terms where S = {k} (i.e., one-digit signatures denoting prime powers p^k) are k=0 and k = A026474(n) = {1,2,4,8,15,22,29..}, because k cannot be the sum of any combination of 3 smaller k. So the only prime power terms are p^0 = 1 and p^A026474(n), or S = {}, {1}, {2}, {4}, {8}, {15}, {22}, {29}...
iii. By induction, once S = {k} is determined, all other terms with the same prime signature appear (or do not) depending on the various combinations of signature exponents of previous terms with smaller signature sums. So for example, terms with the same two-digit signature S = {k,k} (i.e. (pq)^k) are constrained by the following: since p = {1} and q = {1} appear, then (pq) = {1,1} does not because in this case {1}*{1}*{} = {1,1}; since p^2 = {2} and q^2 = {2} appear, then (pq)^2 = {2,2} does not; since {4} appears but {3} does not, then {3,3} appears but {4,4} and {5,5} do not (the latter because {3,3}*{2}*{2} = {5,5} when p^2,q^2 = {2}). Note that {3,3} would not appear if {3,2} appeared because {3,2}*{1}*{} = {3,3} when q = {1}; but because p = {1} and p^2,q^2 = {2} appear, then {2}*{2}*{1} = {3,2} does not. {6,6} does not appear because {6,5} appears (by virtue of other constraints) and {6,5}*{1}*{} = {6,6} when q = {1}. Determining which signatures appear and which do not becomes increasingly complicated as the sequence increases.
Don Reble offered a proof on the Sequence Fans Mailing List which seems to be different (and certainly more formal) than mine. Perhaps mine is more of an "explanation" than a "proof"? (End)

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000028, A026416, A066724, A050376, A084400, A026474.

There are six related sequences: A026477: 1 <= i < j < k < n starting 1,2,3; A026478: 1 <= i <= j <= k < n starting 1,2,3; A026479: 1 <= i < j < k < n starting 1,2,4; A026480: 1 <= i <= j <= k < n starting 1,2,4; A026481: 1 <= i < j < k < n starting 1,3,4; A026482: 1 <= i <= j <= k < n starting 1,3,4.

a = {1, 2, 3}; no = {1 2 3};
Do[x = SelectFirst[Range[Last[a] + 1, 1000], ! MemberQ[no, #] &]; AppendTo[a, x]; no = Union[Times @@@ Subsets[a, {3}]], 200]; a (* Robert Price, May 26 2019 *)

list(lim)=my(v=List(),n,d,k); while(n++<=lim, d=divisors(n); for(i=1,#d-2, if(!setsearch(v,d[i]), next); for(j=i+1,#d-1, if(!setsearch(v,d[j]), next); k=n/(d[i]*d[j]); if(d[j]>=k, break); if(denominator(k)==1 && setsearch(v,k), next(3)))); listput(v,n)); Vec(v) \\ Charles R Greathouse IV, Sep 16 2015

More terms from Christian G. Bower, Nov 15 1999

A051039 4-Stohr sequence.

Original entry on oeis.org

1, 2, 4, 8, 16, 31, 46, 61, 76, 91, 106, 121, 136, 151, 166, 181, 196, 211, 226, 241, 256, 271, 286, 301, 316, 331, 346, 361, 376, 391, 406, 421, 436, 451, 466, 481, 496, 511, 526, 541, 556, 571, 586, 601, 616, 631, 646, 661, 676, 691, 706, 721, 736, 751

Offset: 1

Eric W. Weisstein

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Stoehr Sequence.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A033627, A026474, A051040.

Join[{1,2,4,8},Range[16,3001,15]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)
LinearRecurrence[{2,-1},{1,2,4,8,16,31},60] (* Harvey P. Dale, Dec 25 2016 *)

a(n)=if(n>4,15*n-59,2^(n-1)) \\ Charles R Greathouse IV, Jun 20 2024

a(n) = 15*n-59 for n>4. a(n) = 2*a(n-1)-a(n-2) for n>6. G.f.: x*(7*x^5+4*x^4+2*x^3+x^2+1)/(x-1)^2. - Colin Barker, Sep 19 2012

A051040 5-Stohr sequence.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 63, 94, 125, 156, 187, 218, 249, 280, 311, 342, 373, 404, 435, 466, 497, 528, 559, 590, 621, 652, 683, 714, 745, 776, 807, 838, 869, 900, 931, 962, 993, 1024, 1055, 1086, 1117, 1148, 1179, 1210, 1241, 1272, 1303, 1334, 1365, 1396, 1427

Offset: 1

Eric W. Weisstein

Eric Weisstein's World of Mathematics, Stoehr Sequence.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A062001, A033627, A026474, A051039.

Join[{1,2,4,8,16,32}, Range[63, 2000, 31]] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)
LinearRecurrence[{2,-1},{1,2,4,8,16,32,63},60] (* Harvey P. Dale, Sep 14 2015 *)

a(n)=if(n>6,31*n-154,2^(n-1)) \\ Charles R Greathouse IV, Jun 20 2024

Terms are 2^(n-1) up to a(6) and then 31n-154.

a(n) = 31*n-154 for n>5. a(n) = 2*a(n-1)-a(n-2) for n>7. G.f.: x*(15*x^6+8*x^5+4*x^4+2*x^3+x^2+1)/(x-1)^2. - Colin Barker, Sep 19 2012

Corrected by Henry Bottomley, May 29 2001

A003663 a(n) is smallest number != a(j) + a(k), j < k and a(1) = 1, a(2) = 6.

Original entry on oeis.org

1, 6, 8, 10, 12, 15, 17, 19, 24, 26, 28, 33, 35, 37, 42, 44, 46, 51, 53, 55, 60, 62, 64, 69, 71, 73, 78, 80, 82, 87, 89, 91, 96, 98, 100, 105, 107, 109, 114, 116, 118, 123, 125, 127, 132, 134, 136, 141, 143, 145, 150, 152, 154, 159, 161, 163, 168, 170, 172, 177, 179

Offset: 1

N. J. A. Sloane, Mira Bernstein

nonn

Numbers congruent to {1, 6, 8} mod 9 plus the number 12.

R. K. Guy, "s-Additive sequences", preprint, 1994.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 1..2000
S. R. Finch, Are 0-additive sequences always regular?, Amer. Math. Monthly, 99 (1992), 671-673.
R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy)
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A199162, A060469, A060470, A060471, A060472.

Cf. A003662, A005408, A026471, A026474, A033627, A051039, A051040, A244151.

I:=[1,6,8,10,12,15,17,19,24]; [n le 9 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Feb 22 2018

f[s_List, j_Integer] := Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s, {j}]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[ f[#, 2] &, {1, 6}, 65] (* Robert G. Wilson v, Jul 05 2014 *)
LinearRecurrence[{1,0,1,-1},{1,6,8,10,12,15,17,19,24},70] (* Harvey P. Dale, Jul 25 2018 *)

From Chai Wah Wu, Feb 21 2018: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 9.
G.f.: x*(2*x^8 + x^5 - 3*x^4 + x^3 + 2*x^2 + 5*x + 1)/(x^4 - x^3 - x + 1). (End)

Name clarified by David A. Corneth, Mar 13 2023

A026472 {3, 7} together with the numbers congruent to {1, 2} mod 12.

Original entry on oeis.org

1, 2, 3, 7, 13, 14, 25, 26, 37, 38, 49, 50, 61, 62, 73, 74, 85, 86, 97, 98, 109, 110, 121, 122, 133, 134, 145, 146, 157, 158, 169, 170, 181, 182, 193, 194, 205, 206, 217, 218, 229, 230, 241, 242, 253, 254, 265, 266, 277, 278, 289, 290, 301, 302, 313, 314

Offset: 1

Clark Kimberling

nonn

The old definition of this sequence was "a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)+a(k) for 1<=i<=j<=k<=n". However, Ralf Stephan observes that this does not fit the terms shown. The present definition (due to Stephan) has been adopted as a temporary solution. - N. J. A. Sloane, Nov 24 2004

Regarding the old definition, see Comments at A047239. - Clark Kimberling, Oct 09 2019

Clark Kimberling, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A026476, A026474.

p = {1, 2, 3, 7}; r = 12 Range[200]; Union[p, 1 + r, 2 + r] (* Clark Kimberling, Oct 10 2019 *)

Vec(x*(1 + x + 3*x^3 + 5*x^4 - 3*x^5 + 5*x^6) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Oct 20 2019

From Colin Barker, Oct 10 2019: (Start)
G.f.: x*(1 + x + 3*x^3 + 5*x^4 - 3*x^5 + 5*x^6) / ((1 - x)^2*(1 + x)).
a(n) = a(n-1) + a(n-2) - a(n-3) for n>6.
a(n) = -(39/2) - (5*(-1)^n)/2 + 6*n for n>4.
(End)

More terms from Clark Kimberling, Oct 10 2019

A026476 For n>3, a(n) = 7n - 21 + 2(-1)^n.

Original entry on oeis.org

1, 3, 4, 9, 12, 23, 26, 37, 40, 51, 54, 65, 68, 79, 82, 93, 96, 107, 110, 121, 124, 135, 138, 149, 152, 163, 166, 177, 180, 191, 194, 205, 208, 219, 222, 233, 236, 247, 250, 261, 264, 275, 278, 289, 292, 303, 306, 317, 320, 331, 334, 345, 348, 359, 362, 373, 376

Offset: 1

Clark Kimberling

The old definition of this sequence was "a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)+a(k) for 1<=i<=j<=k<=n". However, Ralf Stephan observes that this does not fit the terms shown. (It produces A109474.) The present definition (due to Stephan) has been adopted as a temporary solution. It would be nice to have a definition similar to the original one. - N. J. A. Sloane, Nov 24 2004
From Philippe Deléham, Nov 21 2016: (Start)
First differences are 2, 1, 5, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11,...
For n>3, numbers that are congruent to 9 or 12 mod 14. (End)

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Yaohui Zhu, Kaiming Sun, Zhengdong Luo, and Lingfeng Wang, Progressive Self-Learning for Domain Adaptation on Symbolic Regression of Integer Sequences, Proc. 39th AAAI Conf. Artif. Intel. (2025) Vol. 39, No. 1, 1692-1699. See p. 1698.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A026472, A026474, A109474.

[1,3,4] cat [7*n - 21 + 2*(-1)^n: n in [4..60]]; // Vincenzo Librandi, Oct 18 2013

CoefficientList[Series[(1 + 2 x + 3 x^3 + 2 x^4 + 6 x^5)/((1 - x)^2 (1 + x)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)

a(n) = if(n>3, 7*n - 21 + 2*(-1)^n, [1,3,4][n]) \\ Charles R Greathouse IV, Nov 21 2016

a(n) = a(n-1)+a(n-2)-a(n-3) for n>6. G.f.: x*(1+2*x+3*x^3+2*x^4+6*x^5)/((1-x)^2*(1+x)). - Colin Barker, May 02 2012

More terms from David Duran (dduran(AT)ashland.edu), Dec 14 2005

A062001 Table by antidiagonals of n-Stohr sequences: T(n,k) is least positive integer not the sum of at most n distinct terms in the n-th row from T(n,1) through to T(n,k-1).

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 4, 4, 2, 1, 5, 7, 4, 2, 1, 6, 10, 8, 4, 2, 1, 7, 13, 15, 8, 4, 2, 1, 8, 16, 22, 16, 8, 4, 2, 1, 9, 19, 29, 31, 16, 8, 4, 2, 1, 10, 22, 36, 46, 32, 16, 8, 4, 2, 1, 11, 25, 43, 61, 63, 32, 16, 8, 4, 2, 1, 12, 28, 50, 76, 94, 64, 32, 16, 8, 4, 2, 1, 13, 31, 57, 91, 125, 127, 64, 32, 16, 8, 4, 2, 1

Offset: 1

Henry Bottomley, May 29 2001

			Array begins as:
  1, 2, 3, 4,  5,  6,  7,   8,   9, ... A000027;
  1, 2, 4, 7, 10, 13, 16,  19,  22, ... A033627;
  1, 2, 4, 8, 15, 22, 29,  36,  43, ... A026474;
  1, 2, 4, 8, 16, 31, 46,  61,  76, ... A051039;
  1, 2, 4, 8, 16, 32, 63,  94, 125, ... A051040;
  1, 2, 4, 8, 16, 32, 64, 127, 190, ... ;
  1, 2, 4, 8, 16, 32, 64, 128, 255, ... ;
  1, 2, 4, 8, 16, 32, 64, 128, 256, ... ;
  1, 2, 4, 8, 16, 32, 64, 128, 256, ... ;
Antidiagonal triangle begins as:
   1;
   2,  1;
   3,  2,  1;
   4,  4,  2,  1;
   5,  7,  4,  2,   1;
   6, 10,  8,  4,   2,   1;
   7, 13, 15,  8,   4,   2,  1;
   8, 16, 22, 16,   8,   4,  2,  1;
   9, 19, 29, 31,  16,   8,  4,  2,  1;
  10, 22, 36, 46,  32,  16,  8,  4,  2, 1;
  11, 25, 43, 61,  63,  32, 16,  8,  4, 2, 1;
  12, 28, 50, 76,  94,  64, 32, 16,  8, 4, 2, 1;
  13, 31, 57, 91, 125, 127, 64, 32, 16, 8, 4, 2, 1;

G. C. Greubel, Antidiagonals n = 1..50, flattened

Rows include A000027, A033627, A026474, A051039, A051040.
Diagonals include A000079, A000225, A033484, A036563, A048487.
Cf. A048488, A048489, A048490, A048491, A139634, A139635, A139697.
A048483 can be seen as half this table.

T[n_, k_]:= If[kG. C. Greubel, May 03 2022 *)

def A062001(n,k):
    if (kA062001(n,k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, May 03 2022

If k <= n+1 then A(n, k) = 2^(k-1), while if k > n+1, A(n, k) = (2^n - 1)*(k - n) + 1 (array).
T(n, k) = A(k, n-k+1) (antidiagonals).
T(2*n-1, n) = A000079(n-1), n >= 1.
T(2*n, n) = A000079(n), n >= 1.
T(2*n+1, n) = A000225(n+1), n >= 1.
T(2*n+2, n) = A033484(n), n >= 1.
T(2*n+3, n) = A036563(n+3), n >= 1.
T(2*n+4, n) = A048487(n), n >= 1.
From G. C. Greubel, May 03 2022: (Start)
T(n, k) = (2^k - 1)*(n-2*k+1) + 1 for k < n/2, otherwise 2^(n-k).
T(2*n+5, n) = A048488(n), n >= 1.
T(2*n+6, n) = A048489(n), n >= 1.
T(2*n+7, n) = A048490(n), n >= 1.
T(2*n+8, n) = A048491(n), n >= 1.
T(2*n+9, n) = A139634(n), n >= 1.
T(2*n+10, n) = A139635(n), n >= 1.
T(2*n+11, n) = A139697(n), n >= 1. (End)

A193911 Sums of the diagonals of the matrix formed by listing the h-Stohr sequences in increasing order.

Original entry on oeis.org

1, 3, 7, 14, 25, 43, 69, 110, 167, 255, 375, 558, 805, 1179, 1681, 2438, 3451, 4975, 7011, 10070, 14153, 20283, 28461, 40734, 57103, 81663, 114415, 163550, 229069, 327355, 458409, 654998, 917123, 1310319, 1834587, 2620998, 3669553, 5242395, 7339525, 10485230

Offset: 1

Jeffrey R. Goodwin, Aug 08 2011

			Portion of the first three rows:
A033627, 2-Stohr  1  2  4  7
A026474, 3-Stohr  1  2  4  8
A051039, 4-Stohr  1  2  4  8
Thus a(1)=1, a(2)=2+1=3, and a(3)=4+2+1=7.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000
Eric Weisstein's World of Mathematics, Stöhr Sequence.
Index entries for linear recurrences with constant coefficients, signature (2,2,-6,1,4,-2).

A193911=t={0,1}; Do[AppendTo[t,t[[-2]]+t[[-1]]]; AppendTo[t,2*t[[-2]]],{n,41}]; Drop[Nest[Accumulate,t,2],1] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)
LinearRecurrence[{2,2,-6,1,4,-2},{1,3,7,14,25,43},40] (* Harvey P. Dale, Jun 20 2015 *)

All h-Stohr sequences have formula: h terms 1,2,..,2^(n-1),..,2^(h-1) and then continue (2^h-1)(n-h)+1. - Henry Bottomley, Feb 04 2000
So we get the sums from the piecewise function:
for odd n>=1, a(n)=2^((n+1)/2)-n+((n+1)/2)-2+Sum_{i=0..((n+1)/2)-1}(2*i+1)*(2^(((n+1)/2)-i) -1);
for even n>=2, a(n)=2^((n/2)+2)-n-4+Sum_{i=0..(n/2)-1}(2*i+1)*(2^((n/2)-i) -1). - Jeffrey R. Goodwin, Aug 09 2011
Let odd m>=3, then a(n)=a(m)-A000295(((m+1)/2)+1), where n>=2 is even. - Jeffrey R. Goodwin, Aug 09 2011
Let even m>=2, then a(n)=a(m)-A077802(m/2)=a(m)-A095151(m/2), where n>=1 is odd. - Jeffrey R. Goodwin, Aug 09 2011
From Alexander R. Povolotsky, Aug 09 2011: (Start)
G.f.: x*(1 + x - x^2)/((-1 + x)^3*(-1 - x + 2*x^2 + 2*x^3)).
a(n+4) = -2*a(n)+3*a(n+2)+n+5.
a(n) = 1/8*(2^(n/2+2)*((10-7*sqrt(2))*(-1)^n+10+7*sqrt(2))-(-1)^n-2*n*(n+12)-79). (End)

A244750 0-additive sequence: a(n) is the smallest number larger than a(n-1) which is not the sum of any subset of earlier terms, with initial values {0, 2, 3, 4}.

Original entry on oeis.org

0, 2, 3, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144

Offset: 1

N. J. A. Sloane and Robert G. Wilson v, Jul 05 2014

			a(5) cannot be 5=2+3. It cannot be 6=2+4. It cannot be 7=3+4, and becomes a(5)=8.
a(6) cannot be 9=2+3+4. It cannot be 10=2+8. It cannot be 11=3+8. It cannot be 12 = 4+8. It cannot be 13=2+3+8. It cannot be 14=2+4+8. It cannot be 15=3+4+8, and becomes a(6)=16.

R. K. Guy, "s-Additive sequences," preprint, 1994.

Steven R. Finch, Are 0-additive sequences always regular?, Amer. Math. Monthly, 99 (1992), 671-673.

Cf. A003662, A003663, A005408, A026471, A026474, A033627, A051039, A051040, A244151, A244749.

Cf. A060469, A060470, A060471, A060472.

A244750:= proc(n)
    option remember;
    if n <= 4 then
        op(n,[0,2,3,4]);
    else
        prev := {seq(procname(k),k=1..n-1)} ;
        for a from procname(n-1)+1 do
            awrks := true ;
            for asub in combinat[choose](prev) do
                if add(p,p=asub) = a then
                    awrks := false;
                    break;
                end if;
            end do:
            if awrks then
                return a;
            end if;
        end do:
    end if;
end proc:
for n from 1 do
    print(A244750(n)) ;
end do: # R. J. Mathar, Jul 12 2014

 f[s_List] := f[n] = Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[ f[#] &, {0, 2, 3, 4}, 16]

Corrected by R. J. Mathar, Jul 12 2014

cp's OEIS Frontend

A276278 Complement of A026474.

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A026477 a(1) = 1, a(2) = 2, a(3) = 3; and for n > 3, a(n) = smallest number > a(n-1) and not of the form a(i)*a(j)*a(k) for 1 <= i < j < k < n.

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A051039 4-Stohr sequence.

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A051040 5-Stohr sequence.

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A003663 a(n) is smallest number != a(j) + a(k), j < k and a(1) = 1, a(2) = 6.

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Magma

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A026472 {3, 7} together with the numbers congruent to {1, 2} mod 12.

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A026476 For n>3, a(n) = 7*n - 21 + 2*(-1)^n.

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A026477 a(1) = 1, a(2) = 2, a(3) = 3; and for n > 3, a(n) = smallest number > a(n-1) and not of the form a(i)a(j)a(k) for 1 <= i < j < k < n.

A026476 For n>3, a(n) = 7n - 21 + 2(-1)^n.