A375690 -id:A375690 - cp's OEIS frontend

A375956 a(0) = 2; for n > 0, a(n) is the smallest palindromic prime containing exactly n more digits on each end than a(n-1), with a(n-1) as the central substring.

2, 727, 1572751, 1081572751801, 100210815727518012001, 1001410021081572751801200141001, 1000141001410021081572751801200141001410001, 100001610001410014100210815727518012001410014100016100001, 1000005310000161000141001410021081572751801200141001410001610000135000001

Offset: 0

Jean-Marc Rebert, Sep 03 2024

a(32) has 1057 digits. - Michael S. Branicky, Sep 29 2024

			a(1) = 727, because 727 is prime and no lesser number verify this property.
As a triangle:
                                     2
                                    727
                                  1572751
                               1081572751801
                           100210815727518012001
                      1001410021081572751801200141001
                1000141001410021081572751801200141001410001
         100001610001410014100210815727518012001410014100016100001
 1000005310000161000141001410021081572751801200141001410001610000135000001

Michael S. Branicky, Table of n, a(n) for n = 0..31

Cf. A375690.

from itertools import count, islice
from sympy import isprime
def A375956_gen(): # generator of terms
    a, l, r = 2, 1, 10
    yield 2
    for n in count(1):
        b = 10**n
        c = b*r
        for i in count(10**(n-1)):
            m = c*i+a*b+int(str(i)[::-1])
            if isprime(m):
                yield m
                a = m
                l += n<<1
                r *= 10**(n<<1)
                break
A375956_list = list(islice(A375956_gen(),20)) # Chai Wah Wu, Sep 27 2024

A376130 a(1) = 3; for n > 1, a(n) is the smallest palindromic prime containing exactly 3 more digits on each end than a(n-1), with a(n-1) as a central substring.

Original entry on oeis.org

3, 1003001, 1021003001201, 1211021003001201121, 1251211021003001201121521, 1211251211021003001201121521121, 1041211251211021003001201121521121401, 1081041211251211021003001201121521121401801, 1091081041211251211021003001201121521121401801901

Offset: 1

Shyam Sunder Gupta, Sep 11 2024

There are 27 terms in this sequence.

Shyam Sunder Gupta, Table of n, a(n) for n = 1..27

Cf. A047076, A053600, A375690, A052205.

A376103 a(1) = 5; for n > 1, a(n) is the smallest palindromic prime containing exactly 2 more digits on each end than a(n-1), with a(n-1) as the central substring.

Original entry on oeis.org

5, 10501, 111050111, 1211105011121, 39121110501112193, 393912111050111219393, 7239391211105011121939327, 79723939121110501112193932797, 157972393912111050111219393279751, 7415797239391211105011121939327975147

Offset: 1

Shyam Sunder Gupta, Sep 10 2024

This is a finite sequence since at a(10) there is no way to add 2 more digits and reach a palindromic prime.

			As a triangle:
          5
        10501
      111050111
    1211105011121
  39121110501112193

Cf. A047076, A053600, A375690, A082563.

cp's OEIS Frontend

A375956 a(0) = 2; for n > 0, a(n) is the smallest palindromic prime containing exactly n more digits on each end than a(n-1), with a(n-1) as the central substring.

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A376130 a(1) = 3; for n > 1, a(n) is the smallest palindromic prime containing exactly 3 more digits on each end than a(n-1), with a(n-1) as a central substring.

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A376103 a(1) = 5; for n > 1, a(n) is the smallest palindromic prime containing exactly 2 more digits on each end than a(n-1), with a(n-1) as the central substring.

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Author

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