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

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

A104386 Numbers k such that the average of the k-th and (k+1)-th primes is a repdigit.

Original entry on oeis.org

2, 3, 4, 25, 29, 603, 6363181, 21366409911, 279238341033925, 2907021742443974, 11220808305309952, 11885037375341198280
Offset: 1

Views

Author

Zak Seidov, Mar 04 2005

Keywords

Crossrefs

Cf. A054268.
Corresponding primes A104387, A104388, repdigits A104389.

Programs

  • Python
    from itertools import count, islice
    from sympy import isprime, prevprime, primepi
    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 primepi(p)
    print(list(islice(agen(), 7))) # Michael S. Branicky, Jun 30 2022

Formula

(prime(k) + prime(k+1))/2 = repdigit.

Extensions

a(8) from Giovanni Resta, Apr 05 2006
a(9) from Michael S. Branicky, Jul 02 2022
a(10)-a(12) from Chai Wah Wu, Jun 01 2024
Showing 1-3 of 3 results.