cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A373170 Main diagonal of A373169.

Original entry on oeis.org

1, 3, 9, 22, 45, 81, 43, 24, 288, 118, 138, 585, 184, 918, 288, 232, 294, 351, 559, 2586, 1179, 3586, 117, 72, 3913, 2949, 5949, 1585, 7239, 8811, 3595, 3789, 3537, 5758, 1968, 18, 6454, 4152, 4374, 1687, 549, 7794, 3922, 8313, 828, 2674, 4251, 2646, 5548, 3636, 3879, 799
Offset: 2

Views

Author

Paolo Xausa, May 28 2024

Keywords

Comments

a(n) is the zeroless analog of the (n-1)-th n-gonal number.

Links

Crossrefs

Cf. A064808, A004719, A373169.

Programs

  • Mathematica
    noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
A373170[n_] := Fold[noz[#2*(n-2) + 1 + #] &, 1, Range[n-2]];
Array[A373170, 100, 2]

Formula

a(n) = A373169(n,n-1).

A243658 a(0)=0; thereafter a(n) = noz(n+a(n-1)), where noz(n) = A004719(n).

Original entry on oeis.org

0, 1, 3, 6, 1, 6, 12, 19, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 21, 42, 64, 87, 111, 136, 162, 189, 217, 246, 276, 37, 69, 12, 46, 81, 117, 154, 192, 231, 271, 312, 354, 397, 441, 486, 532, 579, 627, 676, 726, 777, 829, 882, 936, 991, 147, 24, 82, 141, 21, 82, 144, 27, 91, 156, 222, 289
Offset: 0

Views

Author

N. J. A. Sloane, Jun 11 2014

Keywords

Comments

Zeroless analog of triangular numbers.

Links

Crossrefs

Cf. A004719, A242350, A243063, A243657.
Row n = 3 of A373169.

Programs

  • Maple
    noz:=proc(n) local a,t1,i,j; a:=0; t1:=convert(n,base,10); for i from 1 to nops(t1) do j:=t1[nops(t1)+1-i]; if j <> 0 then a := 10*a+j; fi; od: a; end;
t1:=[0]; for n from 1 to 50 do t1:=[op(t1),noz(n+t1[n])]; od: t1;
  • Mathematica
    noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
Block[{n = 0}, NestList[noz[++n+#] &, 0, 100]] (* Paolo Xausa, Apr 17 2024 *)
  • Python
    from itertools import count, islice
def noz(n): return int(str(n).replace("0", ""))
def agen(): # generator of terms
    yield (an:=0)
    yield from (an:=noz(n+an) for n in count(1))
print(list(islice(agen(), 68))) # Michael S. Branicky, Jul 02 2024

A370812 a(1) = 1; for n >= 2, a(n) = noz(a(n-1) + 2*n - 1), where noz(n) = A004719(n).

Original entry on oeis.org

1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 22, 45, 7, 34, 63, 94, 127, 162, 199, 238, 279, 322, 367, 414, 463, 514, 567, 622, 679, 738, 799, 862, 927, 994, 163, 234, 37, 112, 189, 268, 349, 432, 517, 64, 153, 244, 337, 432, 529, 628, 729, 832, 937, 144, 253, 364, 477
Offset: 1

Views

Author

Paolo Xausa, May 24 2024

Keywords

Comments

Zeroless analog of the positive squares.

Links

Crossrefs

Cf. A000290, A004719, A243657, A243658, A373171, A373172.
Row n = 4 of A373169.

Programs

  • Mathematica
    noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
Block[{n = 1}, NestList[noz[++n*2 - 1 + #] &, 1, 100]]

A373171 a(1) = 1; for n >= 2, a(n) = noz(a(n-1) + 3*n - 2), where noz(n) = A004719(n).

Original entry on oeis.org

1, 5, 12, 22, 35, 51, 7, 29, 54, 82, 113, 147, 184, 224, 267, 313, 362, 414, 469, 527, 588, 652, 719, 789, 862, 938, 117, 199, 284, 372, 463, 557, 654, 754, 857, 963, 172, 284, 399, 517, 638, 762, 889, 119, 252, 388, 527, 669, 814, 962, 1113, 1267, 1424, 1584
Offset: 1

Views

Author

Paolo Xausa, May 28 2024

Keywords

Comments

Zeroless analog of the positive pentagonal numbers.

Links

Crossrefs

Row n = 5 of A373169.
Cf. A000326, A004719, A243658, A370812, A373172.

Programs

  • Mathematica
    noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
Block[{n = 1}, NestList[noz[++n*3 - 2 + #] &, 1, 100]]
  • PARI
    noz(n) = fromdigits(select(sign, digits(n))); \\ A004719
lista(nn) = my(va=vector(nn)); for (n=1, nn, va[n] = if (n==1, 1, noz(va[n-1] + 3*n - 2))); va; \\ Michel Marcus, Jun 03 2024

A373172 a(1) = 1; for n >= 2, a(n) = noz(a(n-1) + 4*n - 3), where noz(n) = A004719(n).

Original entry on oeis.org

1, 6, 15, 28, 45, 66, 91, 12, 45, 82, 123, 168, 217, 27, 84, 145, 21, 9, 82, 159, 24, 19, 18, 111, 28, 129, 234, 343, 456, 573, 694, 819, 948, 181, 318, 459, 64, 213, 366, 523, 684, 849, 118, 291, 468, 649, 834, 123, 316, 513, 714, 919, 1128, 1341, 1558, 1779
Offset: 1

Views

Author

Paolo Xausa, May 28 2024

Keywords

Comments

Zeroless analog of the positive hexagonal numbers.

Links

Crossrefs

Row n = 6 of A373169.
Cf. A000384, A004719, A243658, A370812, A373171.

Programs

  • Mathematica
    noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
Block[{n = 1}, NestList[noz[++n*4 - 3 + #] &, 1, 100]]
nxt[{n_,a_}]:={n+1,FromDigits[DeleteCases[IntegerDigits[a+4n+1],0]]}; NestList[nxt,{1,1},60][[;;,2]] (* Harvey P. Dale, Jul 08 2024 *)
  • PARI
    noz(n) = fromdigits(select(sign, digits(n))); \\ A004719
lista(nn) = my(va=vector(nn)); for (n=1, nn, va[n] = if (n==1, 1, noz(va[n-1] + 4*n - 3))); va; \\ Michel Marcus, Jun 03 2024
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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