A073879 -id:A073879 - cp's OEIS frontend

A073880 a(1) = 1, a(n) = smallest palindrome not included earlier such that a(1)+...+a(n) is a palindrome.

1, 2, 3, 5, 11, 22, 33, 44, 101, 111, 121, 131, 202, 212, 222, 1001, 1111, 1221, 1331, 2002, 2112, 2222, 10001, 10101, 10201, 10301, 11011, 11111, 12021, 13031, 22222, 100001, 101101, 102201, 103301, 110011, 111111, 120021, 130031, 20202, 1000001, 1001001, 1002001, 1003001, 1010101, 1011101, 1012101, 1020201, 2042402, 10000001, 10011001, 10022001, 10033001, 10100101, 10111101, 10200201, 10300301

Offset: 1

Amarnath Murthy, Aug 16 2002

a(57) is likely to be the last term. - Scott R. Shannon, Oct 07 2024
From Robert Israel, Oct 07 2024: (Start)
Proof that a(57) is the last term.
Sum_{i=1..57} a(i) = 91899819.  Suppose r is a palindrome not in {a(1),...,a(56)} such that 91899819 + r is a palindrome.
It has been checked that r must have more digits than 91899819 does.
r can't end in 0 because it's a palindrome. If r ends (and therefore starts) with digit x, then r + 91899819 ends (and starts) with x-1.
But since r + 91899819 > r, that can only happen if r + 91899819 has one more digit than r.
Since r has more digits than 91899819, this implies that r + 91899819 starts with 1 and r starts with 9.
But that's impossible because 9 + 9 ends in 8. (End)

Cf. A073879.

More terms from Giovanni Resta, Feb 08 2006

a(42)-a(57) from Scott R. Shannon, Oct 07 2024

A287662 a(n) is the smallest positive integer not already in sequence such that a(1) + ... + a(n) is a prime power, with a(1) = 1.

Original entry on oeis.org

1, 2, 4, 6, 3, 7, 8, 10, 12, 11, 9, 16, 14, 18, 28, 20, 22, 32, 33, 13, 24, 38, 30, 36, 34, 26, 42, 48, 40, 44, 46, 50, 60, 52, 68, 54, 58, 5, 15, 64, 78, 56, 66, 70, 74, 76, 84, 62, 72, 82, 90, 80, 55, 21, 92, 106, 104, 88, 98, 100, 96, 108, 102, 86, 114, 94, 116, 118, 122, 120, 130, 126, 107, 31, 132, 138

Offset: 1

Ilya Gutkovskiy, May 29 2017

nonn

It appears that the sequence contains all even numbers.

			a(8) = 10 because 1, 2, 3, 4, 6, 7 and 8 have already been used in the sequence, 1 + 2 + 4 + 6 + 3 + 7 + 8 + 5 = 36 is not prime power, 1 + 2 + 4 + 6 + 3 + 7 + 8 + 9 = 40 is not prime power while 1 + 2 + 4 + 6 + 3 + 7 + 8 + 10 = 41 is a prime power.

Cf. A000961, A054408, A073659, A073879, A075562, A084693, A284049.

t = {1}; Do[i = 1; While[! PrimePowerQ[Total[t] + i] || MemberQ[t, i], i++]; AppendTo[t, i], {75}]; t

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

A073880 a(1) = 1, a(n) = smallest palindrome not included earlier such that a(1)+...+a(n) is a palindrome.

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A287662 a(n) is the smallest positive integer not already in sequence such that a(1) + ... + a(n) is a prime power, with a(1) = 1.

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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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