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 1-3 of 3 results.

A104388 Lesser of two successive primes the average of which is a repdigit.

Original entry on oeis.org

3, 5, 7, 97, 109, 4441, 111111109, 555555555551, 9999999999999937, 111111111111111091, 444444444444444419, 555555555555555555491, 777777777777777777777767, 333333333333333333333333333333293, 444444444444444444444444444444444391
Offset: 1

Views

Author

Zak Seidov, Mar 04 2005

Keywords

Crossrefs

Cf. A054268, A104386, A104387 (larger primes), A104389 (repdigits).

Programs

  • Python
    from itertools import count, islice
    from sympy import isprime, prevprime
    def agen():
        for d in count(1):
            ru = int("1"*d)
            for r in range(ru, 10*ru, ru):
                if r > 2:
                    p = prevprime(r)
                    if isprime(r + (r-p)) and prevprime(r+(r-p)) == p:
                        yield p
    print(list(islice(agen(), 15))) # Michael S. Branicky, Jun 30 2022

Formula

a(n) = prime(A104386(n)).

Extensions

More terms from Giovanni Resta, Feb 09 2006

A104387 Larger of two successive primes the average of which is a repdigit.

Original entry on oeis.org

5, 7, 11, 101, 113, 4447, 111111113, 555555555559, 10000000000000061, 111111111111111131, 444444444444444469, 555555555555555555619, 777777777777777777777787, 333333333333333333333333333333373, 444444444444444444444444444444444497
Offset: 1

Views

Author

Zak Seidov, Mar 04 2005

Keywords

Comments

Lesser primes A104388, repdigits A104389. What is the next term?
The next term is 444444444444444444444444444444444497. The first term with more than 100 digits is a(22) which has 109 digits. - Harvey P. Dale, Jun 28 2011

Crossrefs

Programs

  • Mathematica
    Union[Flatten[Table[NextPrime/@Select[FromDigits/@Table[PadLeft[{i},n,i], {n,45}], Mean[{NextPrime[#],NextPrime[#,-1]}]==#&], {i,9}]]] (* Harvey P. Dale, Jun 28 2011 *)
  • Python
    from itertools import count, islice
    from sympy import isprime, prevprime
    def agen():
        for d in count(1):
            ru = int("1"*d)
            for r in range(ru, 10*ru, ru):
                if r > 2:
                    p = prevprime(r)
                    if isprime(r + (r-p)) and prevprime(r+(r-p)) == p:
                        yield 2*r - p
    print(list(islice(agen(), 15))) # Michael S. Branicky, Jun 30 2022

Formula

a(n) = prime(A104386(n)+1).

Extensions

More terms from Giovanni Resta, Apr 05 2006

A104389 Repdigits which are the average of two successive primes.

Original entry on oeis.org

4, 6, 9, 99, 111, 4444, 111111111, 555555555555, 9999999999999999, 111111111111111111, 444444444444444444, 555555555555555555555, 777777777777777777777777, 333333333333333333333333333333333, 444444444444444444444444444444444444
Offset: 1

Views

Author

Zak Seidov, Mar 04 2005

Keywords

Crossrefs

Corresponding primes: A104387, A104388.

Programs

  • Python
    from itertools import count, islice
    from sympy import isprime, prevprime
    def agen():
        for d in count(1):
            ru = int("1"*d)
            for r in range(ru, 10*ru, ru):
                if r > 2:
                    p = prevprime(r)
                    if isprime(r + (r-p)) and prevprime(r+(r-p)) == p:
                        yield r
    print(list(islice(agen(), 15))) # Michael S. Branicky, Jun 30 2022

Formula

a(n) = (A104387(n)+A104388(n))/2.

Extensions

More terms from Giovanni Resta, Apr 05 2006
Showing 1-3 of 3 results.