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.

A154530 Primes that are a concatenation of 2*k and 2*k+1 or 2*k and 2*k-1 for some k.

Original entry on oeis.org

23, 43, 67, 89, 109, 1213, 2221, 2423, 3433, 3637, 4241, 4243, 5051, 5657, 5857, 6263, 6869, 7069, 7877, 7879, 8081, 8887, 9091, 9293, 9697, 10099, 102101, 102103, 108107, 108109, 112111, 114113, 120121, 124123, 126127, 138139, 148147, 150151
Offset: 1

Views

Author

Pierre CAMI, Jan 11 2009

Keywords

Examples

			2*1=2, 2*1+1=3, and 23 the concatenation of 2 and 3 is prime, so a(1)=23

Links

Crossrefs

Cf. A133986, A154531, A328903.
Cf. A010051, subsequence of A248378.

Programs

  • Haskell
    a154530 n = a154530_list !! (n-1)
a154530_list = filter ((== 1) . a010051') a248378_list
-- Reinhard Zumkeller, Jun 27 2015

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010

A328932 Number of primes that are a concatenation of two positive integers whose sum is prime(n).

Original entry on oeis.org

1, 0, 2, 2, 4, 3, 2, 6, 5, 9, 6, 7, 10, 11, 12, 14, 12, 16, 14, 17, 12, 15, 16, 20, 19, 19, 20, 17, 23, 23, 18, 27, 28, 24, 30, 25, 26, 26, 28, 30, 27, 30, 32, 27, 25, 27, 37, 42, 38, 32, 32, 33, 30, 39, 38, 36, 43, 38, 43, 42, 36, 36, 47, 47, 49, 38, 45, 48, 51, 50
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Oct 31 2019

Keywords

Examples

			a(3) = 2 because primes 23, 41 are concatenations of prime(3) = 5 = 2 + 3 = 4 + 1.

Links

Crossrefs

Subsequence of A328903.
Cf. A000040, A066686, A067754.

Programs

  • Maple
    a:= n-> (p-> add(`if`(isprime(parse(cat(i,
        p-i))), 1, 0), i=1..p-1))(ithprime(n)):
seq(a(n), n=1..80);  # Alois P. Heinz, Oct 31 2019

Formula

a(n) = A328903(A000040(n)).

A328948 Number of primes that are a concatenation of two positive integers whose product is n.

Original entry on oeis.org

1, 0, 2, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 2, 0, 0, 2, 1, 0, 3, 1, 0, 2, 1, 0, 2, 2, 0, 1, 2, 0, 3, 0, 0, 0, 1, 0, 2, 1, 0, 2, 1, 0, 1, 2, 0, 1, 2, 0, 3, 1, 0, 2, 0, 0, 3, 1, 0, 1, 0, 0, 4, 1, 0, 3, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 3, 1, 0, 2, 2, 0, 3, 0, 0, 1, 2, 0, 1, 3, 0, 3, 1, 0, 0
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 01 2019

Keywords

Comments

Records: 1, 3, 21, 63, 231, 924, 4389, 5187, 51051, 69069, 127281, 245973, 302841, 969969, 1312311, 1716099. - Corrected by Robert Israel, Dec 14 2023
This is not always the same as the number of divisors d of n such that the concatenation of d and n/d is prime, because the same prime could occur for more than one divisor. For example, 1140678 = 14*81477 = 14814*77 with 1481477 prime, and this prime is counted only once in a(1140678) = 7. - Robert Israel, Dec 14 2023

Examples

			1(11), 2(-), 3(13, 31), 4(41), 5(-), 6(23, 61), 7(17, 71), 8(-), 9(19), 10(101), 11(-), 12(43), 13(113, 131), 14(-), 15(53, 151), 16(-).

Links

Crossrefs

Cf. A000040, A016789, A161904, A328903.

Programs

  • Magma
    [#[a: d in Divisors(n)| IsPrime(a) where a is Seqint(Intseq(d) cat Intseq(n div d))]:n in [1..100]]; // Marius A. Burtea, Nov 05 2019
  • Maple
    f:= proc(n)
   if n mod 3 = 2 then return 0 fi;
   nops(select(isprime, {seq(dcat(t,n/t), t = numtheory:-divisors(n))})
end proc:
map(f, [$1..200]); # Robert Israel, Dec 14 2023
  • PARI
    a(n) = sumdiv(n, d, isprime(eval(concat(Str(d), Str(n/d))))); \\ Michel Marcus, Nov 05 2019

Formula

a(3n + 2) = 0.
Showing 1-3 of 3 results.

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