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 1-8 of 8 results.

A075595 Smallest prime that is obtained by placing digits on both sides of the n-th prime. Or smallest prime that encompasses the n-th prime.

Original entry on oeis.org

127, 131, 151, 173, 1117, 2131, 1171, 1193, 1231, 1291, 1319, 1373, 2411, 1433, 1471, 1531, 1597, 1613, 2671, 2711, 1733, 2791, 1831, 2897, 1973, 21011, 21031, 11071, 11093, 11131, 11273, 11311, 21377, 11393, 11491, 11519, 11579, 11633
Offset: 1

Views

Author

Amarnath Murthy, Sep 28 2002

Keywords

Comments

For small primes, the prefix required is usually 1 or 2.

Links

Crossrefs

Cf. A075596, A075597, A075598, A075599, A075600, A075601, A075602.

Programs

  • Maple
    f:= proc(n) local m,d,d1,v,x,y,y0,z,found;
  m:= ilog10(n);
  v:= infinity;
  for d from 2 do
    for d1 from 1 to d-1 do
      found:= false;
      for x from 10^(d1-1) to 10^d1-1 while not found do
        if d-d1=1 then y0:= 1 else y0:= 10^(d-d1-1)+1 fi;
        for y from y0 to 10^(d-d1)-1 by 2 do
          z:= y+10^(d-d1)*n + 10^(d-d1+m+1)*x;
          if isprime(z) then v:= min(v,z); found:= true; break fi
      od od;
    od;
    if v < infinity then return v fi
  od
end proc:
map(f@ithprime, [$1..100]); # Robert Israel, Aug 28 2018

Extensions

Corrected and extended by Sascha Kurz, Jan 20 2003

A075598 a(1) = 5 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).

Original entry on oeis.org

5, 151, 11519, 2115193, 121151939, 21211519397, 4212115193971, 342121151939719, 43421211519397199, 2434212115193971993, 224342121151939719937, 122434212115193971993787, 51224342121151939719937871, 2512243421211519397199378719, 325122434212115193971993787197, 93251224342121151939719937871973
Offset: 1

Views

Author

Amarnath Murthy, Sep 28 2002

Keywords

Links

Crossrefs

Cf. A075595, A075596, A075597, A075599, A075600, A075601, A075602.

Programs

  • Maple
    f:= proc(n) local m,d,d1,v,x,y,y0,z,found;
  m:= ilog10(n);
  v:= infinity;
  for d from 2 do
    for d1 from 1 to d-1 do
      found:= false;
      for x from 10^(d1-1) to 10^d1-1 while not found do
        if d-d1=1 then y0:= 1 else y0:= 10^(d-d1-1)+1 fi;
        for y from y0 to 10^(d-d1)-1 by 2 do
          z:= y+10^(d-d1)*n + 10^(d-d1+m+1)*x;
          if isprime(z) then v:= min(v,z); found:= true; break fi
      od od;
    od;
    if v < infinity then return v fi
  od
end proc:
A[1]:= 5:
for n from 2 to 20 do
  A[n]:= f(A[n-1])
od:
seq(A[n],n=1..20); # Robert Israel, Aug 28 2018

Extensions

More terms from Sascha Kurz, Jan 20 2003
Terms a(13) and beyond from Robert Israel, Aug 28 2018

A075596 a(1) = 2 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).

Original entry on oeis.org

2, 127, 11273, 1112731, 411127319, 34111273199, 3341112731993, 233411127319933, 32334111273199339, 3323341112731993391, 633233411127319933919, 66332334111273199339193, 1663323341112731993391937
Offset: 1

Views

Author

Amarnath Murthy, Sep 28 2002

Keywords

Crossrefs

Cf. A075595, A075597, A075598, A075599, A075600, A075601, A075602.

Extensions

More terms from Sascha Kurz, Jan 20 2003
One more term from David Wasserman, Jan 20 2005

A075599 a(1) = 7 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).

Original entry on oeis.org

7, 173, 11731, 2117317, 421173173, 34211731733, 1342117317337, 813421173173377, 28134211731733771, 4281342117317337713, 142813421173173377131, 21428134211731733771317, 2214281342117317337713171, 2022142813421173173377131711, 1120221428134211731733771317111
Offset: 1

Views

Author

Amarnath Murthy, Sep 28 2002

Keywords

Crossrefs

Cf. A075595, A075596, A075597, A075598, A075600, A075601, A075602.

Extensions

More terms from Sascha Kurz, Jan 20 2003
Further terms from Ray G. Opao, Nov 26 2004
a(14)-a(15) corrected by Sean A. Irvine, Feb 26 2025

A075600 a(1) = 11 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).

Original entry on oeis.org

11, 1117, 211177, 12111773, 1121117731, 1112111773139, 811121117731399, 18111211177313993, 5181112111773139933, 351811121117731399339, 63518111211177313993399, 11635181112111773139933991
Offset: 1

Views

Author

Amarnath Murthy, Sep 28 2002

Keywords

Crossrefs

Cf. A075595, A075596, A075597, A075598, A075599, A075601, A075602.

Extensions

More terms from Sascha Kurz, Jan 20 2003

A075601 a(1) = 13 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).

Original entry on oeis.org

13, 2131, 121313, 51213137, 3512131379, 135121313797, 21351213137977, 5213512131379777, 352135121313797771, 63521351213137977713, 16352135121313797771319, 9163521351213137977713193
Offset: 1

Views

Author

Amarnath Murthy, Sep 28 2002

Keywords

Crossrefs

Cf. A075595, A075596, A075597, A075598, A075599, A075600, A075602.

Extensions

Corrected and extended by Sascha Kurz, Jan 23 2003

A075602 a(1) = 17 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).

Original entry on oeis.org

17, 1171, 211711, 32117117, 6321171179, 263211711799, 42632117117999, 6426321171179993, 564263211711799931, 15642632117117999311, 1156426321171179993119, 311564263211711799931199
Offset: 1

Views

Author

Amarnath Murthy, Sep 28 2002

Keywords

Crossrefs

Cf. A075595, A075596, A075597, A075598, A075599, A075600, A075601.

Extensions

More terms from Sascha Kurz, Jan 23 2003

A082563 a(1) = 3; for n>=1, a(n+1) is the smallest palindromic prime with a(n) as a central substring.

Original entry on oeis.org

3, 131, 11311, 121131121, 1212113112121, 36121211311212163, 303612121131121216303, 7230361212113112121630327, 30723036121211311212163032703, 723072303612121131121216303270327, 1472307230361212113112121630327032741, 114723072303612121131121216303270327411
Offset: 1

Views

Author

Benoit Cloitre, May 04 2003

Keywords

Comments

The minimal nested palindromic primes with seed 3; see A261881 for a guide to related sequences.

Examples

			As a triangle:
........3
.......131
......11311
....121131121
..1212113112121
36121211311212163

Links

Crossrefs

Cf. A053600, A075597, A261881.

Programs

  • Mathematica
    s = {3}; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {15}]; s
(* Peter J. C. Moses, Sep 01 2015 *)

Extensions

Name changed by Arkadiusz Wesolowski, Sep 15 2011
More terms from Clark Kimberling, Sep 23 2015
Showing 1-8 of 8 results.

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