A217386 -id:A217386 - cp's OEIS frontend

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

Jonathan Vos Post, Oct 02 2012

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.

			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.

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

Cf. A000217, A004086, A006567, A217386.

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 *)

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

More terms from Alois P. Heinz, Oct 03 2012

A217591 Absolute differences between emirps (A006567) and their reversals.

Original entry on oeis.org

18, 54, 18, 36, 54, 36, 18, 18, 594, 198, 792, 594, 594, 792, 792, 198, 396, 396, 594, 594, 594, 198, 396, 198, 396, 594, 594, 198, 198, 198, 792, 594, 198, 792, 594, 792, 7992, 180, 270, 2268, 540, 8532, 810, 6804, 1908, 7902, 360, 2358, 630, 2718, 180, 1908, 5904, 1998, 7992, 90, 6084, 8172, 8262, 8442

Offset: 1

Jonathan Vos Post, Oct 07 2012

This is unsorted, and in order of appearance of emirps.

All values are multiples of 18 (A008600). - Charles R Greathouse IV, Oct 15 2012

			a(1) = absolute value of first emirp versus its reversal = |13 - 31| = |-18| = 18.
a(2) = |17 - 71| = |-54| = 54.
a(3) = |31 - 13| = |18| = 18.
a(4) = |37 - 73| = |-36| = 36.

Cf. A004086, A006567, A008600, A217286, A217386, A217387.

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
q:= n-> isprime(n) and (p-> p<>n and isprime(p))(R(n)):
map(x-> abs(x-R(x)), select(q, [$2..1280]))[];  # Alois P. Heinz, Jul 12 2024

a(n) = | A006567(n) - R(A006567(n)) | = | A006567(n) - A004086(A006567(n)) |.

Corrected and more terms from Georg Fischer, Jul 12 2024

A217610 Emirps (A006567) whose difference with the reversal is a perfect 4th power (A000583).

Original entry on oeis.org

1100090011, 1100900011, 1103093011, 1103903011, 1154094511, 1154904511, 1213093121, 1213903121, 1304094031, 1304904031, 1364094631, 1364904631, 1367097631, 1367907631, 1421091241, 1421901241, 1450090541, 1450900541, 1466096641, 1466906641, 1495095941, 1495905941, 1498098941, 1498908941

Offset: 1

Jonathan Vos Post, Oct 06 2012

This is to A217387 as perfect 4th powers (A000583) are to perfect cubes (A000578), and as A217386 is to perfect squares (A000290). Subset of A217386, since every perfect 4th power is a perfect square (though not vice versa). In these terms all the difference are equal to 30^4.

Values a(1) through a(24) supplied by Giovanni Resta.

Cf. A004086, A006567, A217286, A217386, A217387, 217591.

cp's OEIS Frontend

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

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A217591 Absolute differences between emirps (A006567) and their reversals.

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A217610 Emirps (A006567) whose difference with the reversal is a perfect 4th power (A000583).

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