A073880 -id:A073880 - cp's OEIS frontend

A073879 a(1) = 1, a(n) = smallest number not included earlier such that a(1)+...+a(n) is a palindrome.

1, 2, 3, 5, 11, 22, 33, 24, 10, 20, 30, 41, 40, 50, 21, 60, 31, 70, 51, 81, 80, 61, 71, 91, 90, 112, 110, 220, 330, 231, 440, 550, 121, 660, 341, 770, 451, 671, 880, 561, 781, 891, 882, 100, 200, 300, 410, 400, 500, 210, 600, 310, 700, 510, 810, 800, 610, 710, 910

Offset: 1

Amarnath Murthy, Aug 16 2002

Ivan Neretin, Table of n, a(n) for n = 1..8323 (all terms before the sum exceeds 10^12)

Cf. A073880.

seq={1}; Do[s=Total[seq]; k=1; While[MemberQ[seq, k] || !PalindromeQ[s+k], k++]; AppendTo[seq, k], {i,1,50}]; seq (* Amiram Eldar, Dec 04 2018 *)

ispal(n)={my(v=digits(n));for(i=1, #v\2, if(v[i]<>v[#v+1-i], return(0))); 1}
seq(n)={my(v=vector(n), M=Map(), t=0); for(n=1, n, for(k=1, oo, if(!mapisdefined(M,k) && ispal(k+t), mapput(M,k,1); v[n]=k; t+=k; break))); v} \\ Andrew Howroyd, Dec 04 2018

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jun 24 2003

A109872 Palindromes such that successive difference of terms is also a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 202, 303, 404, 505, 606, 707, 808, 909, 1111, 2112, 3113, 4114, 5115, 6116, 7117, 8118, 9119

Offset: 1

Amarnath Murthy, Jul 09 2005

The final term is a(36) = 9119 - see A073880. - Scott R. Shannon, Oct 07 2024

			1111 follows 909 as 1111-909 = 202.

Cf. A073880.

a(29) onwards corrected by Scott R. Shannon, Oct 07 2024

A376856 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that a(n), |a(n) - a(n-1)| and a(1) + ... +a(n) are all palindromes.

Original entry on oeis.org

1, 2, 3, 5, 11, 22, 33, 44, 121, 222, 101, 202, 454, 1221, 2222, 1001, 2002, 4554, 12221, 22222, 10001, 20002, 45554, 122221, 222222, 100001, 200002, 455554, 1222221, 2222222, 1000001, 2000002, 4555554, 12222221, 22222222, 10000001, 20000002, 45555554, 122222221, 222222222, 100000001, 200000002, 455555554, 1222222221, 2222222222, 1000000001

Offset: 1

Scott R. Shannon, Oct 06 2024

The sequence is infinite as from a(13) onward a repetitive pattern of five numbers appears, 45...54, 12...21, 22...22, 10...01, 20...02, all of which grow by one extra digit each iteration.

			a(9) = 121 as 121 is a palindrome, |121 - 44| = 77 is a palindrome, and 1 + 2 + 3 + 5 + 11 + 22 + 33 + 44 + 121 = 242 is a palindrome.

Cf. A073880, A073879, A002113, A369127, A361335, A347402.

cp's OEIS Frontend

A073879 a(1) = 1, a(n) = smallest number not included earlier such that a(1)+...+a(n) is a palindrome.

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A109872 Palindromes such that successive difference of terms is also a palindrome.

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A376856 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that a(n), |a(n) - a(n-1)| and a(1) + ... +a(n) are all palindromes.

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