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.

A243362 Numbers n such that A243361(n) = 123456789.

Original entry on oeis.org

54023, 54203, 500407, 23456789, 23458679, 23459687, 23465789, 23465987, 23469587, 23475869, 23478569, 23489657, 23495867, 23496587, 23498567, 23546879, 23546987, 23548697, 23564897, 23564987, 23567849, 23569487, 23576489, 23584679, 23587649, 23589647, 23594687
Offset: 1

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Author

Jaroslav Krizek, Jun 04 2014

Keywords

Comments

Supersequence of A243363, A243364 and A160402.
Conjecture 1: sequence is infinite.
Conjecture 2: a(1), a(2) and a(3) are composites; there are no other numbers n > 3 such that a(n) = composite number.

Examples

			Sets of divisors of a(n): (1, 89, 607, 54023); (1, 67, 809, 54203); (1, 83, 6029, 500407); (1, 23456789); …
		

Crossrefs

Programs

  • Magma
    [n: n in [1..1000000] | Seqint(Reverse(Sort(&cat[(Intseq(k)): k in Divisors(n)]))) eq 123456789];

Formula

a(1) = 54023; a(2) = 54203; a(3) = 500407; a(4) … a(3101) = A160402; a(3102) ... a(22659) = A243363; ....

A243364 Primes whose reverse concatenation of divisors (A176558) contains all the digits 1-9 exactly once; the number of digits 0 is arbitrary (in base 10).

Original entry on oeis.org

23456789, 23458679, 23459687, 23465789, 23465987, 23469587, 23475869, 23478569, 23489657, 23495867, 23496587, 23498567, 23546879, 23546987, 23548697, 23564897, 23564987, 23567849, 23569487, 23576489, 23584679, 23587649, 23589647, 23594687, 23645879, 23645987
Offset: 1

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Author

Jaroslav Krizek, Jun 04 2014

Keywords

Comments

Sequence differs from A160402; a(n) = A160402(n) for first 3098 terms, a(3099) = 203457869.
Subsequence of A243362. Supersequence of A160402 and A243363.
Primes p such that A243361(p) = 123456789.
Conjecture: sequence is infinite.

Examples

			Prime 200000000003456789 is in sequence because A176558(200000000003456789) = 2000000000034567891; each digit 1 - 9 appears exactly once.
		

Crossrefs

Formula

a(1) ... a(3098) = A160402; a(3099) ... a(22656) = A243363; ...

A255596 Distinct-digit primes that are the concatenation of m and prime(m) for some number m.

Original entry on oeis.org

23, 47, 613, 1237, 1759, 27103, 35149, 45197, 57269, 58271, 61283, 85439, 93487, 145829, 147853, 2371489, 3152087, 3902687, 4062791, 5614073, 5914327, 7405639, 8356421
Offset: 1

Views

Author

Zak Seidov, Mar 25 2015

Keywords

Examples

			The last term is a(23) = 8356421 (prime) because all 7 digits are different and m=835 with 6421=prime(m).
		

Crossrefs

Programs

  • Mathematica
    Select[FromDigits[IntegerDigits@ #~Join~IntegerDigits[Prime@ #]] & /@
    Range@ 1200, PrimeQ@ # && Max@ DigitCount@ # == 1 &] (* Michael De Vlieger, Mar 25 2015 *)

A256339 Distinct-digit primes that are concatenation of prime(m) and m for some m.

Original entry on oeis.org

53, 239, 6719, 7321, 4073561, 6257813, 6521843, 85271063
Offset: 1

Views

Author

Zak Seidov, Mar 25 2015

Keywords

Comments

The last term is a(8) = 85271063 (prime) because all 8 digits are different and m=1063 with 8527=prime(m).

Crossrefs

Subsequence of A029743 (distinct-digit primes).

Programs

  • Mathematica
    Select[FromDigits[IntegerDigits[Prime@ #]~Join~IntegerDigits@ #] & /@
    Range@ 1200, PrimeQ@ # && Max@ DigitCount@ # == 1 &] (* Michael De Vlieger, Mar 25 2015 *)
Showing 1-4 of 4 results.