A282811 Numbers n such that n and n + 1 are both composite and the reverse of n and n + 1 are both prime.

34, 91, 118, 124, 133, 145, 300, 361, 364, 370, 376, 391, 721, 730, 745, 754, 763, 775, 778, 784, 790, 904, 916, 931, 943, 973, 994, 1003, 1015, 1075, 1081, 1084, 1099, 1105, 1126, 1138, 1189, 1204, 1255, 1261, 1324, 1348, 1351, 1393, 1444, 1477

Offset

1,1

Comments

Related to a palindrome, a semordnilap is a word that when reversed results in a new, different, valid word. For example the semordnilap of the word "desserts" is the word "stressed". Applying this principle to numbers, any number is either a palindrome or a semordnilap. This sequence deals with adjacent composite numbers whose semordnilap numbers are prime.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

For n = 2 * 17 = 34, which reverses to 43, a prime, we have n + 1 = 5 * 7 = 35, which reverses to 53, also a prime.

Mathematica

searchMax = 2000; Select[Complement[Range[searchMax], Prime[Range[PrimePi[searchMax]]]], Not[PrimeQ[# + 1]] && PrimeQ[FromDigits[Reverse[IntegerDigits[#]]]] && PrimeQ[FromDigits[Reverse[IntegerDigits[# + 1]]]] &] (* Alonso del Arte, Feb 23 2017 *)
Select[Partition[Range[1500], 2, 1], AllTrue[#, CompositeQ] && AllTrue[ IntegerReverse[#], PrimeQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 10 2017 *)

Prog

(PARI) rev(n)=fromdigits(Vecrev(digits(n)))
is(n)=isprime(rev(n)) && isprime(rev(n+1)) && !isprime(n) && !isprime(n+1) \\ Charles R Greathouse IV, Feb 23 2017

Crossrefs

Sequence in context: A140602 A067977 A183311 * A185460 A260467 A202421

Adjacent sequences: A282808 A282809 A282810 * A282812 A282813 A282814

Keyword

nonn,base

Author

Philip Mizzi, Feb 22 2017

Status

approved