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.

A248378 a(2n) = concatenation of n+1 with n+2, a(2n+1) = concatenation of n+2 with n+1.

Original entry on oeis.org

12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 910, 109, 1011, 1110, 1112, 1211, 1213, 1312, 1314, 1413, 1415, 1514, 1516, 1615, 1617, 1716, 1718, 1817, 1819, 1918, 1920, 2019, 2021, 2120, 2122, 2221, 2223, 2322, 2324, 2423, 2425, 2524, 2526
Offset: 0

Views

Author

N. J. A. Sloane, Oct 07 2014

Keywords

References

  • Charles Duvall, Email to N. J. A. Sloane, Oct 07 2014.

Links

Crossrefs

Cf. A001704, A127423.
Cf. A154530 (primes).

Programs

  • Haskell
    import Data.List (transpose)
a248378 n = a248378_list !! n
a248378_list = concat $ transpose [a001704_list, tail a127423_list]
-- Reinhard Zumkeller, Oct 07 2014
  • Mathematica
    Table[{FromDigits[Join[IntegerDigits[n],IntegerDigits[n+1]]],FromDigits[Join[IntegerDigits[n+1],IntegerDigits[ n]]]},{n,30}]//Flatten (* Harvey P. Dale, Apr 19 2024 *)

A328903 Number of primes that are a concatenation of two positive integers whose sum is n.

Original entry on oeis.org

0, 0, 1, 0, 2, 2, 0, 2, 3, 0, 3, 4, 0, 3, 5, 0, 4, 2, 0, 6, 5, 0, 4, 5, 0, 6, 7, 0, 6, 9, 0, 6, 8, 0, 9, 8, 0, 7, 7, 0, 9, 10, 0, 11, 2, 0, 12, 12, 0, 10, 11, 0, 11, 14, 0, 3, 10, 0, 10, 12, 0, 16, 12, 0, 16, 14, 0, 14, 19, 0, 13, 17, 0, 12, 16, 0, 15, 2, 0
Offset: 0

Views

Author

Juri-Stepan Gerasimov, Oct 30 2019

Keywords

Comments

First n > 1 with n != 0 (mod 3) and a(n) = 0 is n = 4477. - Alois P. Heinz, Oct 30 2019

Examples

			1(-), 2(11), 3(-), 4(13, 31), 5(23, 41), 6(-), 7(43, 61), 8(17, 53, 71), 9(-), 10(19, 37, 73), 11(29, 47, 83, 101), 12(-), 13(67, 103, 211), ...

Links

Crossrefs

Cf. A000040, A008486, A008585, A066686, A067574, A154530, A328932.

Programs

  • Maple
    a:= proc(n) option remember; `if`(irem(n, 3)=0, 0, add(
     `if`(isprime(parse(cat(i, n-i))), 1, 0), i=1..n-1))
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Oct 30 2019

Formula

a(n) = 0 if n = 1 or n == 0 (mod 3). - Alois P. Heinz, Oct 30 2019

Extensions

More terms from Alois P. Heinz, Oct 30 2019

A154531 Primes that are a concatenation of consecutive primes in two ways.

Original entry on oeis.org

199211, 211199, 233239, 239233, 257263, 263257, 353359, 359353, 523541, 541523, 653659, 659653, 971977, 977971, 19731979, 19791973, 23332339, 23392333, 32593271, 32713259, 36373643, 36433637, 37613767, 37673761, 42834289, 42894283, 49934999, 49994993
Offset: 1

Views

Author

Pierre CAMI, Jan 11 2009

Keywords

Examples

			233 and 239 consecutive primes, 233239 and 239233 are both primes.

Links

Crossrefs

Cf. A133986, A154530.

Programs

  • Mathematica
    ccp2[{a_,b_}]:=Module[{c=a*10^IntegerLength[b]+b,d=b*10^IntegerLength[a]+ a}, If[ AllTrue[ {c,d}, PrimeQ],{c,d},{}]]; ccp2/@Partition[Prime[ Range[ 1000]],2,1]//Flatten (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 20 2017 *)

Extensions

Corrected by Harvey P. Dale, Feb 20 2017
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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