A087581 -id:A087581 - cp's OEIS frontend

A051934 a(n) is the smallest palindrome > a(n-1) such that a(1)+a(2)+...+a(n) is a prime.

2, 3, 6, 8, 22, 66, 242, 252, 262, 414, 444, 626, 676, 686, 808, 2442, 2552, 2992, 4664, 4884, 6006, 6226, 6666, 8228, 20202, 20302, 20402, 40204, 40304, 60606, 61116, 61716, 80608, 202202, 207702, 212212, 402204, 405504, 609906, 619916, 623326, 801108

Offset: 1

Felice Russo, Dec 21 1999

a(n) is even except for n = 2. - Chai Wah Wu, Aug 30 2021

Chai Wah Wu, Table of n, a(n) for n = 1..186 (terms 1..100 from Reinhard Zumkeller)

Cf. A002113, A010051, A051896, A087581.

a051934 n = a051934_list !! (n-1)
a051934_list = f 0 a002113_list where
   f x (m:ms) | a010051 (x + m) == 1 = m : f (x + m) ms
              | otherwise            = f x ms
-- Reinhard Zumkeller, Dec 28 2011

palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t = {s = 2}; Do[If[palQ[n] && PrimeQ[x = s + n], AppendTo[t, n]; s = x], {n, 3, 815000}]; t (* Jayanta Basu, Jun 24 2013 *)
sp[{t_,a_}]:=Module[{k=a+1},While[!PalindromeQ[k]||!PrimeQ[t+k],k++];{t+k,k}]; NestList[ sp,{2,2},50][[;;,2]] (* Harvey P. Dale, Jul 08 2024 *)

Missing a(29)=40304 inserted by Reinhard Zumkeller, Dec 28 2011

A087582 Primes such that successive differences are distinct palindromes.

Original entry on oeis.org

2, 3, 5, 11, 19, 23, 67, 89, 311, 523, 937, 1229, 1471, 1559, 1811, 1877, 2281, 2543, 3037, 3319, 3793, 4217, 4651, 5297, 5569, 5801, 6427, 6871, 7477, 8093, 8779, 9587, 10223, 10687, 10889, 11717, 12373, 13049, 13907, 16349, 17167, 17863, 18701

Offset: 0

Amarnath Murthy, Sep 17 2003

Conjecture: Sequence is infinite and every even palindrome is a member.

			The sequence of successive difference is 1,2,6,8,4,44,22,222,212,414...

Cf. A087581.

More terms from David Wasserman, Jun 13 2005

A087583 Distinct primes such that the absolute values of successive differences are distinct palindromes. a(n+1) is chosen to be < a(n) if such a prime exists, minimizing a(n)-a(n+1); otherwise the minimal a(n+1) > a(n) is chosen.

Original entry on oeis.org

2, 3, 5, 11, 7, 29, 37, 103, 59, 271, 19, 107, 349, 127, 359, 157, 419, 137, 409, 701, 277, 691, 257, 661, 197, 641, 167, 773, 97, 733, 239, 1087, 461, 1117, 431, 1097, 643, 1259, 613, 1451, 967, 149, 977, 281, 2393, 61, 919, 41, 929, 31, 839, 3061, 619, 1487

Offset: 0

Amarnath Murthy, Sep 17 2003

The sequence of absolute differences is 1,2,6,4,22,8,66,44.... Conjecture: this sequence is infinite and contains every even palindrome.

			a(3) = 11: |11-5| = 6, a palindrome. The primes < 5 are excluded because they have already occurred in the sequence. 7 is excluded because |7-5| = 2 has already occurred as a difference.

Cf. A087581, A087582.

Edited and extended by David Wasserman, Jun 14 2005

cp's OEIS Frontend

A051934 a(n) is the smallest palindrome > a(n-1) such that a(1)+a(2)+...+a(n) is a prime.

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A087582 Primes such that successive differences are distinct palindromes.

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A087583 Distinct primes such that the absolute values of successive differences are distinct palindromes. a(n+1) is chosen to be < a(n) if such a prime exists, minimizing a(n)-a(n+1); otherwise the minimal a(n+1) > a(n) is chosen.

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