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

1,1

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.

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000217, A004086, A006567, A217386.

Sequence in context: A197241 A332948 A224505 * A282784 A332912 A361491

Adjacent sequences: A217283 A217284 A217285 * A217287 A217288 A217289

Keyword

nonn,base,easy

Author

Jonathan Vos Post, Oct 02 2012

Extensions

More terms from Alois P. Heinz, Oct 03 2012

Status

approved