A115884 -id:A115884 - cp's OEIS frontend

A115885 The n-th prime minus n gives a palindrome.

1, 2, 3, 4, 5, 6, 8, 32, 55, 57, 61, 71, 90, 95, 99, 114, 116, 126, 135, 137, 171, 173, 182, 230, 349, 399, 415, 457, 488, 610, 653, 739, 903, 951, 997, 1010, 1036, 1050, 1231, 1396, 1478, 1508, 1542, 1612, 1660, 1906, 1948, 2032, 2092, 2152, 2242

Offset: 1

Giovanni Resta, Feb 06 2006

			p(126)-126=575.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A084122, A115884.

palQ[n_]:=Module[{digs=IntegerDigits[Prime[n]-n]},digs==Reverse[digs]]; Select[Range[2400],palQ] (* Harvey P. Dale, Dec 15 2011 *)

A115888 Palindromes equal to the sum of a prime number with its index.

Original entry on oeis.org

3, 5, 8, 11, 101, 242, 383, 424, 454, 545, 585, 606, 666, 676, 757, 949, 2552, 3443, 3663, 4664, 5445, 6006, 6886, 9339, 10001, 10601, 11411, 12321, 15551, 15651, 17871, 17971, 18281, 21412, 22622, 22922, 24642, 24942, 25752, 26762, 28582

Offset: 1

Giovanni Resta, Feb 06 2006

			666 = prime(103)+103.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A014688, A115884.

Subsequence of A002113.

Select[Total/@Table[{n,Prime[n]},{n,3200}],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 03 2017 *)

ispal(n) = my(e=digits(n));e == Vecrev(e) \\ A002113
for(k=1,10^6, b=k+prime(k);if(ispal(b),print1(b,", "))) \\ Alexandru Petrescu, Jun 15 2022

A173638 The n-th semiprime plus n gives a palindrome in base 10.

Original entry on oeis.org

1, 2, 11, 17, 20, 23, 25, 35, 40, 48, 53, 59, 69, 86, 94, 100, 128, 133, 138, 141, 145, 194, 211, 216, 224, 232, 282, 326, 450, 615, 665, 824, 876, 929, 1171, 1197, 1267, 1290, 1293, 1450, 1498, 1520, 1566, 1655, 1790, 1898, 2248, 2313, 2624, 2786, 2826, 2849, 2912, 3058, 3082, 3098, 3270, 3290, 3408, 3586, 3610, 3672, 3792, 3912, 3945, 3982, 4000

Offset: 1

Jonathan Vos Post, Nov 23 2010

This is to semiprimes A001358 as A115884 is to primes A000040.

			a(1) = 1 because 1st semiprime = 4, 4+1=5 is trivially a palindrome.
a(2) = 2 because 2nd semiprime = 6, 6+2=8 is trivially a palindrome.
a(3) = 11 because 11th semiprime = 33, 33+11=44 is nontrivially a palindrome.
a(4) = 17 because 17th semiprime = 49, 49+17=66 is nontrivially a palindrome.
a(5) = 20 because 20th semiprime = 57, 57+20=77 is nontrivially a palindrome.
a(8) = 35 because 35th semiprime = 106, 106+35=141 is nontrivially a palindrome.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

A001358, A002113, A115884, A100493.

Module[{nn=20000,sems},sems=Select[Range[nn],PrimeOmega[#]==2&]; Select[ Thread[{Range[Length[sems]],sems}],Total[ #]==IntegerReverse[Total[ #]]&]] [[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 08 2016 *)

{n: n + A001358(n) is in A002113} == {n: n + A001358(n) = R(n)} == {n: n + A001358(n) = A004086(n)}.

A115901 Numbers k such that prime(k) - k and prime(k) + k are palindromes.

Original entry on oeis.org

1, 2, 3, 4, 71, 116, 7271, 43585895

Offset: 1

Giovanni Resta, Feb 06 2006

Intersection of A115884 and A115885.

			prime(43585895) - 43585895 = 806494608 and
prime(43585895) + 43585895 = 893666398.

Cf. A115884, A115885.

A116037 n+p(n)+p(p(n)) is a palindrome, where p(n) denotes the n-th prime.

Original entry on oeis.org

1, 17, 20, 29, 253, 344, 370, 445, 479, 675, 786, 887, 1539, 3115, 4221, 4271, 6002, 6416, 7657, 9015, 10003, 11563, 12651, 12984, 14200, 14494, 14880, 14928, 15504, 15738, 17064, 18008, 18265, 18395, 19065, 21795, 23093, 23676, 24078, 24570

Offset: 1

Giovanni Resta, Feb 13 2006

			10003+p(10003)+p(p(10003)) = 1481841.

Cf. A115884.

cp's OEIS Frontend

A115885 The n-th prime minus n gives a palindrome.

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A115888 Palindromes equal to the sum of a prime number with its index.

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A173638 The n-th semiprime plus n gives a palindrome in base 10.

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A115901 Numbers k such that prime(k) - k and prime(k) + k are palindromes.

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A116037 n+p(n)+p(p(n)) is a palindrome, where p(n) denotes the n-th prime.

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