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 1-7 of 7 results.

A104421 Numbers n such that n, prime(n), prime(n)+n, prime(n)-n and prime(n)*n all numbers without the digit 1.

Original entry on oeis.org

74, 75, 80, 86, 87, 95, 96, 350, 352, 354, 355, 357, 360, 364, 376, 536, 557, 564, 583, 584, 590, 592, 593, 594, 596, 599, 600, 623, 635, 639, 656, 659, 660, 665, 667, 674, 677, 678, 699, 700, 703, 706, 707, 724, 728, 734, 744, 750, 759, 762, 765, 766, 770
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

The graph is of quasi-piecewise linear character.
Any other reasonable function(s) of p and m not having digit 1?
Subsequence of A084368: a(1) = 75 = A084368(36), a(100) = 2744 = A084368(898). - Zak Seidov, Dec 04 2013

Examples

			For n = 74, p = prime(74) = 373, p + n = 447, p - n = 299, p*n = 27602.
For n = 256709, p = prime(256709) = 3599737, p + n = 3856446, p - n = 3343028, p*n = 924084885533.

Links

Crossrefs

Cf. A038603, A084368, A104419-A104428.

Programs

  • Mathematica
    id[x_]:=IntegerDigits[x]; pr[i_]:=Prime[i]; ra=Range[3000]; A104421=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 1]=={}&]
prQ[n_]:=With[{p=Prime[n]},AllTrue[IntegerDigits/@{n,p,p+n,p-n,p*n},FreeQ[#,1]&]]; Select[Range[1000],prQ] (* Harvey P. Dale, Aug 29 2025 *)

A104422 Numbers n such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 2-less.

Original entry on oeis.org

5, 6, 16, 18, 30, 36, 78, 81, 83, 90, 94, 95, 100, 103, 104, 105, 108, 110, 111, 114, 131, 133, 136, 137, 139, 153, 154, 159, 160, 166, 488, 489, 495, 496, 498, 499, 500, 510, 511, 514, 640, 641, 643, 644, 645, 646, 650, 665, 669, 671, 680, 685, 687, 688, 690
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

From the first 3000 primes, only 182 are such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 2-less.

Links

Crossrefs

Cf. A104419-A104428.

Programs

  • Mathematica
    id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104422=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 2]=={}&]
tlQ[n_]:=DigitCount[n,10,2]==0; Select[Range[700],AllTrue[{#,p=Prime[#], p+#,p-#,p*#},tlQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 09 2018 *)

A104423 Numbers n such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 3-less.

Original entry on oeis.org

5, 7, 8, 20, 25, 26, 45, 47, 50, 95, 100, 101, 102, 105, 107, 109, 110, 121, 145, 149, 155, 156, 158, 160, 161, 165, 167, 168, 169, 171, 177, 180, 181, 205, 209, 210, 271, 272, 275, 277, 279, 284, 288, 290, 292, 297, 299, 628, 629, 745, 751, 761, 764, 765, 769
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

From the first 3000 primes, only 200 are such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 3-less.

Crossrefs

Cf. A104419-A104428.

Programs

  • Mathematica
    id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104423=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 3]=={}&]

A104424 Numbers n such that n, prime(n), prime(n)+n, prime(n)-n and prime(n)*n all lack the digit 4.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 10, 22, 23, 26, 27, 28, 29, 31, 39, 57, 58, 62, 66, 112, 120, 122, 125, 126, 129, 130, 131, 135, 137, 139, 152, 153, 178, 182, 183, 192, 196, 210, 211, 212, 213, 216, 220, 221, 222, 250, 280, 285, 286, 287, 291, 293, 295, 299, 300, 303, 305, 306
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

From the first 3000 primes, only 289 are such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 4-less.

Links

Crossrefs

Cf. A104419-A104428.

Programs

  • Maple
    fourless:= n -> not has(4,convert(n,base,10)):
p:= 1: R:= NULL: count:= 0:
for n from 1 while count < 100 do
  p:= nextprime(p);
  if andmap(fourless, [n, p, p+n, p-n, p*n]) then
    count:= count+1; R:= R, n;
  fi
od:
R; # Robert Israel, Apr 23 2020
  • Mathematica
    id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104424=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 4]=={}&]
Select[Range[350],Count[Flatten[IntegerDigits/@{#,Prime[#],Prime[ #]+#,Prime[ #]-#,Prime[ #]#}],4]==0&] (* Harvey P. Dale, Apr 13 2022 *)

Extensions

Name edited by Robert Israel, Apr 23 2020

A104425 Numbers n such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 5-less.

Original entry on oeis.org

1, 4, 6, 7, 9, 10, 11, 18, 19, 23, 27, 29, 30, 32, 40, 41, 42, 43, 44, 49, 60, 61, 63, 67, 69, 70, 73, 74, 79, 80, 110, 111, 131, 140, 143, 144, 166, 170, 171, 179, 180, 181, 183, 184, 187, 189, 193, 196, 199, 200, 201, 202, 206, 209, 223, 228, 229, 233, 261, 263, 270
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

From the first 3000 primes, only 369 are such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 5-less.

Crossrefs

Cf. A104419-A104428.

Programs

  • Mathematica
    id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104425=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 5]=={}&]
flQ[n_]:=Module[{pr=Prime[n]},Union[DigitCount[{n,pr,pr+n,pr-n,pr*n},10,5]] == {0}]; Select[Range[300],flQ] (* Harvey P. Dale, May 29 2014 *)

A104427 Numbers n such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 7-less.

Original entry on oeis.org

1, 2, 3, 5, 10, 11, 13, 23, 24, 29, 30, 32, 35, 38, 43, 46, 51, 60, 62, 81, 82, 98, 100, 140, 146, 180, 185, 188, 189, 190, 191, 200, 202, 205, 209, 215, 221, 226, 231, 246, 252, 254, 255, 261, 266, 281, 282, 291, 293, 301, 320, 321, 323, 346, 369, 381, 382, 391
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

From the first 3000 primes, only 200 are such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 7-less.

Crossrefs

Cf. A104419-A104428.

Programs

  • Mathematica
    id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104427=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 7]=={}&]

A104426 Numbers k such that the digit 6 does not appear in the decimal expansion of k, Pk, Pk+k, Pk-k, or Pk*k, where Pk is the k-th prime.

Original entry on oeis.org

1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 25, 30, 33, 35, 37, 41, 43, 44, 48, 50, 51, 52, 53, 54, 55, 58, 70, 72, 75, 80, 81, 82, 83, 85, 93, 95, 128, 149, 152, 170, 171, 174, 184, 185, 187, 188, 189, 194, 198, 201, 203, 210, 212, 215, 217, 233, 235, 238, 242, 245
Offset: 1

Views

Author

Zak Seidov, Mar 07 2005

Keywords

Comments

From the first 3000 primes, only 179 are terms.
From the first 3000 integers, only 343 are terms.

Crossrefs

Cf. A052414, A104419, A104420, A104421, A104422, A104423, A104424, A104425, A104427, A104428.

Programs

  • Mathematica
    id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[3000];A104426=Select[ra, Position[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]], 6]=={}&]
slQ[n_]:=Module[{p=Prime[n]},Union[DigitCount[#,10,6]&/@{n,p,p+n,p-n, p*n}] == {0}]; Select[Range[250],slQ] (* Harvey P. Dale, Feb 01 2018 *)
  • PARI
    has(n)=!setsearch(Set(digits(n)),6)
is(n,p=prime(n))=has(n) && has(p) && has(p+n) && has(p-n) && has(p*n) \\ Charles R Greathouse IV, Feb 01 2018

Extensions

Definition modified (at the suggestion of N. J. A. Sloane) by Harvey P. Dale, Feb 10 2018
Showing 1-7 of 7 results.

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

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