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.

A053582 a(n+1) is the smallest prime ending with a(n), where a(1)=1.

Original entry on oeis.org

1, 11, 211, 4211, 34211, 234211, 4234211, 154234211, 3154234211, 93154234211, 2093154234211, 42093154234211, 342093154234211, 11342093154234211, 3111342093154234211, 63111342093154234211, 2463111342093154234211, 232463111342093154234211
Offset: 1

Views

Author

G. L. Honaker, Jr., Jan 18 2000

Keywords

Examples

			The least prime ending with seed 1 is 11; the least prime ending with 11 is 211; the least prime ending with 211 is 4211. - _Clark Kimberling_, Sep 17 2015
		

Crossrefs

Programs

  • Maple
    R:= 1: v:= 1:
    for iter from 1 to 30 do
    d:= ilog10(v)+1;
    for x from v+10^d by 10^d do
      if isprime(x) then R:= R, x; v:= x; break fi
    od
    od:
    R; # Robert Israel, Sep 24 2020
  • Mathematica
    f[n_] := f[n] = Block[{j = f[n - 1], k = 1, l = Floor[Log[10, f[n - 1]] + 1]},   While[m = k*10^l + j; ! PrimeQ@ m, k++ ]; m]; f[1] = 1; Array[f, 17]
    nxt[n_]:=Module[{k=1,p=10^IntegerLength[n]},While[!PrimeQ[k*p+n],k++];k*p+n]; NestList[nxt,1,20] (* Harvey P. Dale, Jul 14 2016 *)
  • Python
    from sympy import isprime
    from itertools import count, islice
    def agen(an=1): # generator of terms
        while True:
            yield an
            pow10 = 10**len(str(an))
            for t in count(pow10+an, step=pow10):
                if isprime(t):
                    an = t
                    break
    print(list(islice(agen(), 18))) # Michael S. Branicky, Jun 23 2022

Extensions

a(14)-a(17) corrected by Robert G. Wilson v, Dec 07 2010

A053583 a(n+1) is the smallest prime ending with (but not equal to) a(n), where a(1)=3.

Original entry on oeis.org

3, 13, 113, 2113, 12113, 612113, 11612113, 1611612113, 111611612113, 1111611612113, 81111611612113, 2181111611612113, 132181111611612113, 11132181111611612113, 3411132181111611612113, 413411132181111611612113, 12413411132181111611612113
Offset: 1

Views

Author

G. L. Honaker, Jr., Jan 18 2000

Keywords

Crossrefs

Programs

  • Maple
    A[1]:= 3;
    for n from 2 to 100 do
    d:= 10^(ilog10(A[n-1])+1);
    for k from 1 do
      p:= A[n-1]+d*k;
      if isprime(p) then
        A[n]:= p;
        break
      fi
    od
    od:
    seq(A[n],n=1..100); # Robert Israel, Jul 15 2014
  • Python
    from sympy import isprime
    from itertools import count, islice
    def agen(an=3):
        while True:
            yield an
            pow10 = 10**len(str(an))
            for t in count(pow10+an, step=pow10):
                if isprime(t):
                    an = t
                    break
    print(list(islice(agen(), 17))) # Michael S. Branicky, Jun 23 2022

Extensions

Definition corrected by Robert Israel, Jul 15 2014

A069612 a(1) = 19 (the smallest prime ending in a 9) and a(n+1) = smallest prime ending in a(n).

Original entry on oeis.org

19, 419, 5419, 35419, 435419, 11435419, 111435419, 9111435419, 89111435419, 1389111435419, 81389111435419, 381389111435419, 15381389111435419, 3315381389111435419, 153315381389111435419, 22153315381389111435419, 2022153315381389111435419
Offset: 1

Views

Author

Amarnath Murthy, Mar 27 2002

Keywords

Crossrefs

Programs

  • Mathematica
    w=9; Table[w; i=1; While[PrimeQ[ToExpression[StringJoin[ToString[i], ToString[w]]]]==False, i++ ]; w=ToExpression[StringJoin[ToString[i], ToString[w]]], {32}]
    nxt[n_]:=Module[{c=10^IntegerLength[n],x=1},While[!PrimeQ[c*x+n],x++];c*x+n]; NestList[nxt,19,15] (* Harvey P. Dale, Sep 25 2013 *)
  • Python
    from sympy import isprime
    from itertools import count, islice
    def agen(an=19):
        while True:
            yield an
            pow10 = 10**len(str(an))
            for t in count(pow10+an, step=pow10):
                if isprime(t):
                    an = t
                    break
    print(list(islice(agen(), 17))) # Michael S. Branicky, Jun 23 2022

Extensions

More terms from Hans Havermann, Jun 06 2002

A077715 a(1) = 7; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists.

Original entry on oeis.org

7, 17, 317, 6317, 26317, 126317, 2126317, 72126317, 372126317, 5372126317, 305372126317, 9305372126317, 409305372126317, 20409305372126317, 100020409305372126317, 9100020409305372126317, 209100020409305372126317, 40209100020409305372126317
Offset: 1

Views

Author

Amarnath Murthy, Nov 19 2002

Keywords

Comments

a(n) is the smallest prime obtained by prefixing a(n-1) with a number of the form d*10^k where d is a single digit, 0 < d < 10, and k >= 0. Conjecture: d*10^k always exists.

Crossrefs

Programs

  • Maple
    a:= proc(n) option remember; local k, m, d, p;
          if n=1 then 7 else k:= a(n-1);
            for m from length(k) do
              for d to 9 do p:= k +d*10^m;
                if isprime(p) then return p fi
            od od
          fi
        end:
    seq(a(n), n=1..20);  # Alois P. Heinz, Jan 12 2015
  • Python
    from sympy import isprime
    from itertools import islice
    def agen(an=7):
        while True:
            yield an
            pow10 = 10**len(str(an))
            while True:
                found = False
                for t in range(pow10+an, 10*pow10+an, pow10):
                    if isprime(t):
                        an = t; found = True; break
                if found: break
                pow10 *= 10
    print(list(islice(agen(), 18))) # Michael S. Branicky, Jun 23 2022

Extensions

More terms from Ray Chandler, Jul 23 2003
Definition clarified by N. J. A. Sloane, Jan 19 2015
Showing 1-4 of 4 results.