A227410 -id:A227410 - cp's OEIS frontend

A227413 a(1)=1, a(2n)=nthprime(a(n)), a(2n+1)=nthcomposite(a(n)), where nthprime = A000040, nthcomposite = A002808.

1, 2, 4, 3, 6, 7, 9, 5, 8, 13, 12, 17, 14, 23, 16, 11, 10, 19, 15, 41, 22, 37, 21, 59, 27, 43, 24, 83, 35, 53, 26, 31, 20, 29, 18, 67, 30, 47, 25, 179, 58, 79, 34, 157, 54, 73, 33, 277, 82, 103, 40, 191, 62, 89, 36, 431, 114, 149, 51, 241, 75, 101, 39, 127, 46

Offset: 1

Antti Karttunen, Jul 10 2013

Inverse permutation of A135141.

Shares with A073846 the property that the other bisection consists of just primes and the other bisection of just nonprimes.

Antti Karttunen and Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entries for sequences that are permutations of the natural numbers

Similarly constructed permutations: A227402, A227404, A227410, A227412. Cf. also A073846, A209636.

import Data.List (transpose)
a227413 n = a227413_list !! (n-1)
a227413_list = 1 : concat (transpose [map a000040 a227413_list,
                                      map a002808 a227413_list])
-- Reinhard Zumkeller, Jan 29 2014

a(1)=1, a(2n) = A000040(a(n)), a(2n+1) = A002808(a(n)).

A007097(n) = a(A000079(n)).

A227411 Palindromic prime numbers representing a date in "condensed European notation" DDMMYY.

Original entry on oeis.org

10301, 10501, 10601, 30103, 30203, 30403, 30703, 30803, 31013, 70207, 70507, 70607, 90709, 91019

Offset: 1

Shyam Sunder Gupta, Sep 22 2013

For February, the number of days will be 28 only, as year cannot be a leap year for DDMMYY to be a prime number.
The sequence is finite, with 14 terms. The largest term is a(14)=91019.
There are no 6-digit solutions - the month must be 11 and the day cannot start with a 0 or a 2. Nor can the day start with a 1 because this makes the palindrome of the form 1x11x1 - divisible by 1001. This leaves only 301103, which is 11*31*883, so not prime. - Jon Perry, Sep 23 2013

			a(1)=10103 is prime and represents a date in DDMMYY format as 010103.

Cf. A213182, A227407, A227410.

palindromicQ[n_] := TrueQ[IntegerDigits[n] == Reverse[IntegerDigits[n]]]; t = {}; Do[If[m < 8, If[OddQ[m], b = 31, If[m == 2, b = 28, b = 30]], If[OddQ[m], b = 30, b = 31]]; Do[a = 100 m + y + 10000 d; If[PrimeQ[a] && palindromicQ[a], AppendTo[t, a]], {d, 1, b}], {m, 1, 12}, {y, 1, 99}]; Union[t]

Incorrect a(15)-a(32) from Vincenzo Librandi, Sep 23 2013 removed. - Jon Perry, Sep 24 2013

cp's OEIS Frontend

A227413 a(1)=1, a(2n)=nthprime(a(n)), a(2n+1)=nthcomposite(a(n)), where nthprime = A000040, nthcomposite = A002808.

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