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 1-4 of 4 results.

A048549 a(n+1) is next smallest prime beginning with a(n), initial prime is 2.

Original entry on oeis.org

2, 23, 233, 2333, 23333, 2333321, 233332117, 2333321173, 233332117313, 23333211731399, 2333321173139903, 2333321173139903173, 23333211731399031733, 2333321173139903173301, 2333321173139903173301021
Offset: 1

Views

Author

Patrick De Geest, May 15 1999

Keywords

Links

Crossrefs

Cf. A048550, A048551, A048552, A048553, A048554, A048555, A048556, A030456.
Similar to but different from A069603.

Programs

  • Mathematica
    b = 10; s = {{2}};
Do[NestWhile[# + 1 &, 0, ! (PrimeQ[FromDigits[tmp = Join[Last[s], (nn = #;
IntegerDigits[nn - Sum[b^n, {n, l = NestWhile[# + 1 &, 1, ! (nn - (Sum[b^n, {n, #}]) < 0) &] - 1}], b, l + 1])], b]]) &]; AppendTo[s, tmp], {20}]; Map[FromDigits, s] (* Peter J. C. Moses, Aug 06 2015 *)

A068167 Define an increasing sequence as follows. Given the first term, called the seed (which need not share the property of the remaining terms), subsequent terms are obtained by inserting at least one digit in the previous term so as to obtain the smallest number with the specified property. This is the prime sequence with the seed a(1) = 2.

Original entry on oeis.org

2, 23, 223, 1223, 10223, 102023, 1020023, 10200263, 102002603, 1020026303, 10200226303, 102002263031, 1020002263031, 10200022363031, 102000223263031, 1020000223263031, 10200002232630131, 102000022326301313, 1020000222326301313, 10200002223236301313
Offset: 1

Views

Author

Amarnath Murthy, Feb 25 2002

Keywords

Examples

			The primes that can be obtained by inserting/placing a digit in a(2) = 23 are 223, 233, 239, 263, 283, 293, etc. a(3) = 223 is the smallest.

Links

Crossrefs

Cf. A068166, A030456.

Programs

  • Maple
    a:= proc(n) option remember; local s, w, m;
      if n=1 then 2
    else w:=a(n-1); s:=""||w; m:=length(s);
         min(select(x->length(x)=m+1 and isprime(x),
         {seq(seq(parse(cat(seq(s[h], h=1..i), j,
         seq(s[h], h=i+1..m))), j=0..9), i=0..m)})[])
      fi
    end:
seq(a(n), n=1..23);  # Alois P. Heinz, Nov 07 2014

Extensions

Corrected and extended by Robert Gerbicz, Sep 06 2002

A254718 a(n) is the least semiprime having a(n-1) as a substring, a(1)=4.

Original entry on oeis.org

4, 14, 141, 1141, 11141, 111413, 1111413, 11114137, 111114137, 1111141373, 11111141373, 111111413737, 1111114137373, 11111141373734, 1111114137373402, 11111141373734023, 111111413737340234, 11111114137373402349, 111111114137373402349, 1111111141373734023499
Offset: 1

Views

Author

Zak Seidov, Feb 06 2015

Keywords

Examples

			4=2*2, 14=2*7, 141=3*47, 1141=7*163, 11141=13*857, 111413=43*2591, 1111413=3*370471, 11114137=47*236471, 111114137=31*3584327, 1111141373=1051*1057223.

Links

Crossrefs

Cf. A001358, A030456.

Extensions

a(11)-a(20) from Jon E. Schoenfield, Feb 19 2015

A360534 Lexicographically earliest sequence of distinct prime numbers such that among each pair of consecutive terms, the decimal expansion of the smallest term appears in that of the largest term.

Original entry on oeis.org

2, 23, 3, 13, 113, 11, 211, 2111, 22111, 322111, 3221, 32213, 2213, 22133, 622133, 6221, 62213, 362213, 5362213, 5, 53, 353, 3533, 33533, 333533, 33353, 233353, 233, 2333, 23333, 323333, 3233333, 32333333, 632333333, 6323, 86323, 863, 3863, 33863, 1338637, 7
Offset: 1

Views

Author

Rémy Sigrist, Feb 10 2023

Keywords

Comments

This sequence is infinite:
- if a(n) < 10^k, then 10^(k+1) and 10*a(n) + 1 are coprime,
- so, by Dirichlet's theorem on arithmetic progressions, there are infinitely many prime numbers of the form k*10^(k+1) + 10*a(n) + 1, and we can extend the sequence.
If we consider positive integers instead of prime numbers, then we obtain the powers of 10 (A011557).

Examples

			The first terms are:
  n   a(n)    a(n) aligned
  --  ------  ------------
   1       2        2
   2      23        23
   3       3         3
   4      13        13
   5     113       113
   6      11       11
   7     211      211
   8    2111      2111
   9   22111     22111
  10  322111    322111
  11    3221    3221
  12   32213    32213
  13    2213     2213
  14   22133    22133
  15  622133   622133

Links

Crossrefs

Cf. A011557, A030456, A335043.

Programs

  • PARI
    See Links section.
Showing 1-4 of 4 results.

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