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.

A101115 Beginning with the n-th prime, the number of successive times a new prime can be formed by prepending the smallest nonzero digit.

Original entry on oeis.org

0, 5, 0, 9, 5, 4, 8, 4, 5, 9, 4, 6, 2, 7, 6, 8, 9, 7, 6, 3, 14, 5, 5, 2, 4, 10, 1, 5, 7, 3, 4, 3, 5, 5, 0, 6, 5, 8, 5, 13, 4, 5, 4, 5, 3, 8, 4, 4, 5, 8, 3, 6, 1, 4, 4, 2, 5, 2, 2, 3, 4, 9, 8, 7, 4, 7, 3, 3, 5, 5, 7, 8, 4, 3, 3, 2, 1, 7, 0, 4, 3, 5, 3, 7, 9, 6, 6, 5, 6, 8
Offset: 1

Views

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004

Keywords

Comments

It is possible the procedure described would generate some left-truncatable primes (A024785). Although zero digits cannot be added, it is possible the starting prime may contain zeros. Therefore the possible number of digit additions is not limited by the length of the largest known left-truncatable prime. Further, because the smallest digit that satisfies the requirement is used each time, it is possible that choosing a larger digit would allow more single digits to be added. Therefore although some of the set of left-truncatable primes may be generated by this practice, not all of them will.
In principle it is possible that some a(n) is undefined because the process could go on indefinitely, but this is very unlikely. The largest a(n) for n <= 300000 is a(49120) = 18. - Robert Israel, Jun 29 2015

Examples

			a(2) is 5 because the second prime is 3, to which single nonzero digits can be prepended 5 times yielding a new prime each time (giving preference to the smallest digit that satisfies the requirement): 13, 113, 2113, 12113, 612113 (see A053583). There is no nonzero digit which can be prepended to 612113 to yield a new prime.
a(21) = 14 because the 21st prime (73) can be prepended with single nonzero digits 14 times yielding a new prime each time: 73, 173, 6173, 66173, ..., 4818372912366173.

Links

Crossrefs

Cf. A053583, A024785, A000040, A101116, A101117, A101118.

Programs

  • Maple
    f:= proc(n) local p, nd, d, count, x, success;
      p:= ithprime(n); nd:= ilog10(p);
      for count from 0 do
        nd:= nd+1;
        success:= false;
        for d from 1 to 9 do
          x:= 10^nd * d + p;
          if isprime(x) then
             success:= true;
             break
          fi
        od;
        if not success then return(count) fi;
        p:= x;
      od
end proc:
map(f, [$1..100]); # Robert Israel, Jun 29 2015
  • Python
    from sympy import isprime, prime
def a(n):
    pn = prime(n)
    s, c, found = str(pn), 0, True
    while found:
        found = False
        for d in "123456789":
            if isprime(int(d+s)):
                s, c, found = d+s, c+1, True
                break
    return c
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Jun 24 2022

A101116 Values in A101115 which are records.

Original entry on oeis.org

0, 5, 9, 14, 15, 18, 19, 20, 22
Offset: 1

Views

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004

Keywords

Comments

All primes up to 1000003 have been tested.

Crossrefs

Cf. A053583, A024785, A000040, A101115, A101117, A101118.

Programs

  • Python
    from sympy import isprime, nextprime
def agen(): # generator of tuple of terms of (A101116, A101117, A101118)
    n, pn, record = 0, 1, -1
    while True:
        n += 1
        pn = nextprime(pn)
        s, c, found = str(pn), 0, True
        while found:
            found = False
            for d in "123456789":
                if isprime(int(d+s)):
                    s, c, found = d+s, c+1, True
                    break
        if c > record:
            record = c
            yield record, pn, int(s)
g = agen()
print([next(g)[0] for n in range(1, 7)]) # Michael S. Branicky, Jun 24 2022

Extensions

a(7)-a(8) from Michael S. Branicky, Jun 24 2022
a(9) from Michael S. Branicky, Jul 26 2024

A101117 a(n) = the first prime yielding the record value A101116(n).

Original entry on oeis.org

2, 3, 7, 73, 13799, 600307, 77197951, 4866134641, 36052921903
Offset: 1

Views

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004

Keywords

Examples

			a(6) = 600307 because 600307 is the first prime to which A101116(6) digits (18) can be prepended yielding a new prime each time (giving preference to the smallest digit which meets the requirement) - 600307, 3600307, 93600307, ..., 9912733515196363393600307.

Crossrefs

Cf. A053583, A024785, A000040, A101115, A101116, A101118.

Programs

  • Python
    g = agen() # uses agen() and imports from A101116
print([next(g)[1] for n in range(1, 7)]) # Michael S. Branicky, Jun 24 2022

Extensions

a(7)-a(8) from Michael S. Branicky, Jun 24 2022
a(9) from Michael S. Branicky, Jul 26 2024

A259848 Suffixes of 4818372912366173 (all primes).

Original entry on oeis.org

3, 73, 173, 6173, 66173, 366173, 2366173, 12366173, 912366173, 2912366173, 72912366173, 372912366173, 8372912366173, 18372912366173, 818372912366173, 4818372912366173
Offset: 1

Views

Author

José de Jesús Camacho Medina, Aug 17 2015

Keywords

Examples

			.......................3
.......................73
.......................173
.......................6173
.......................66173
.......................366173
.......................2366173
.......................12366173
.......................912366173
.......................2912366173
.......................72912366173
.......................372912366173
.......................8372912366173
.......................18372912366173
.......................818372912366173
.......................4818372912366173

Links

Crossrefs

Cf. A101115, A101118.

Formula

a(n) = 4818372912366173 mod 10^n.
Showing 1-4 of 4 results.

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