A217286 Larger of pairs of emirps (A006567) whose difference with the (smaller) reversal is a triangular number (A000217).

73, 1811, 7817, 7927, 11701, 12611, 14431, 14831, 15101, 15241, 15541, 15601, 16111, 16451, 16651, 17021, 18671, 18731, 19181, 19541, 19681, 19841, 32213, 32713, 33223, 33623, 33923, 35803, 36013, 36353, 36913, 37123, 37363, 37463, 37963, 39383, 39983, 71707

Offset: 1

Author

Jonathan Vos Post, Oct 02 2012

Keywords

• nonn
• base
• easy

Comments

Related to A217386 as triangular numbers (A000217) are to squares (A000290), but in the current sequence, only the larger of each emirp pair is used.

Examples

			a(1) = 73 because 73 - 37 = 36 = 8th triangular number.
a(2) = 1811 because R(1811) = A004086(1811) = 1181, and 1811 - 1181 = 630 = 35th triangular number.
a(3) = 7817 because 7817 - 7187 = 630 = 35th triangular number.
a(4) = 7927 because 7927 - 7297 = 630 = 35*36/2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000217, A004086, A006567, A217386.

Programs

Mathematica

emrp[p_]:=Module[{rev=IntegerReverse[p]},If[rev!=p&&PrimeQ[rev],Max[ rev,p],Nothing]]; Select[Union[emrp/@Prime[Range[7500]]],OddQ[Sqrt[8(#-IntegerReverse[ #])+1]]&] (* Harvey P. Dale, Jan 30 2023 *)

Formula

{k: k is in A006567 and k - A004086(k) is in A000217}.

Extensions

More terms from Alois P. Heinz, Oct 03 2012