A135697 -id:A135697 - cp's OEIS frontend

A138070 Triangle read by rows: row n lists the successive digits of A135697(n), the palindromic number formed from the reflected decimal expansion of Pi.

3, 3, 3, 3, 1, 3, 3, 1, 1, 3, 3, 1, 4, 1, 3, 3, 1, 4, 4, 1, 3, 3, 1, 4, 1, 4, 1, 3, 3, 1, 4, 1, 1, 4, 1, 3, 3, 1, 4, 1, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 9, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 9, 9, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 9, 2, 9, 5, 1, 4, 1, 3

Offset: 1

Omar E. Pol, Mar 03 2008

Also, successive digits of A135697(n).

			Triangle begins:
      3
     3,3
    3,1,3
   3,1,1,3
  3,1,4,1,3

Paolo Xausa, Table of n, a(n) for n = 1..11325 (rows 1..150 of triangle, flattened).

Decimal expansion of Pi: A000796. Cf. A135697, A135698, A138071.

Table[Join[#[[;; Floor[n/2]]], #[[Ceiling[n/2] ;; 1 ;; -1]]], {n, Length[#]}] & [First[RealDigits[Pi, 10, 15]]] (* Paolo Xausa, Dec 09 2024 *)

A039954 Palindromic primes formed from the reflected decimal expansion of Pi.

Original entry on oeis.org

3, 313, 31415926535897932384626433833462648323979853562951413

Offset: 1

G. L. Honaker, Jr.

Carlos Rivera reports that the next two members of this sequence have 301 and 921 digits. The first has been tested with APRTE-CLE. The second one is only a StrongPseudoPrime at the moment. - May 16 2003
Thomas Spahni reports that the fifth member of this sequence with 921 digits is prime. He used Francois Morain's ECPP-V6.4.5a which proved primality in 14913.7 seconds running on a Celeron Core2 CPU at 2.00GHz. - Jun 05 2008
Primes in A135697. Terms with an odd number of digits are the primes in A135698. - Omar E. Pol, Mar 06 2012

C. K. Caldwell and G. L. Honaker, Jr., Prime Curios!, 31414...51413 (53-digits)
Shyam Sunder Gupta, Mystery of pi, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 19, 473-497.
Eric Weisstein's World of Mathematics, Palindromic Prime.

Cf. A002385, A119351, A135697, A135698.

Select[Table[p = Flatten[RealDigits[Pi, 10, d]]; (FromDigits[p] - 1)*10^(Length[p] - 3) + FromDigits[Drop[Reverse[p], 2]], {d, 27}], PrimeQ] (* Arkadiusz Wesolowski, Dec 18 2011 *)

A135698 Palindromes with odd number of digits formed from the reflected decimal expansion of Pi.

Original entry on oeis.org

3, 313, 31413, 3141413, 314151413, 31415951413, 3141592951413, 314159262951413, 31415926562951413, 3141592653562951413, 314159265353562951413, 31415926535853562951413, 3141592653589853562951413, 314159265358979853562951413, 31415926535897979853562951413

Offset: 1

Omar E. Pol, Mar 01 2008, Mar 28 2008

Pi = 3.14159265358979323846264338327... (see A000796).
The number of digits of a(n) is equal to 2n - 1.
The first five members of this sequence are in the example of A119351.

			n ........... a(n)
1 ............ 3
2 ........... 313
3 .......... 31413
4 ......... 3141413
5 ........ 314151413
6 ....... 31415951413
7 ...... 3141592951413
8 ..... 314159262951413
9 .... 31415926562951413
10 .. 3141592653562951413

G. C. Greubel, Table of n, a(n) for n = 1..250

Cf. A000796, A002113, A119351.

Cf. A135697, A039954.

pinxt[n_]:=With[{pid=RealDigits[Pi,10,20][[1]]},Module[{a=Take[pid,n]}, FromDigits[Join[a,Reverse[Most[a]]]]]]; Table[pinxt[n],{n,1,15}] (* Harvey P. Dale, Oct 06 2011 *)

More terms from Harvey P. Dale, Oct 06 2011

A138071 Triangle read by rows: row n lists the digits of A135698(n), the palindromic number with odd number of digits formed from the reflected decimal expansion of Pi.

Original entry on oeis.org

3, 3, 1, 3, 3, 1, 4, 1, 3, 3, 1, 4, 1, 4, 1, 3, 3, 1, 4, 1, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 9, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 9, 2, 9, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 9, 2, 6, 2, 9, 5, 1, 4, 1, 3, 3, 1, 4, 1, 5, 9, 2, 6, 5, 6, 2, 9, 5, 1, 4, 1, 3

Offset: 1

Omar E. Pol, Mar 03 2008

Also, successive digits of the numbers A135698(n).

			Triangle begins:
              3
           3, 1, 3
        3, 1, 4, 1, 3
     3, 1, 4, 1, 4, 1, 3
  3, 1, 4, 1, 5, 1, 4, 1, 3

Paolo Xausa, Table of n, a(n) for n = 1..10000 (rows 1..100 of triangle, flattened).

Decimal expansion of Pi: A000796. Cf. A119351, A135697, A135698, A138070.

Table[Join[#[[;; n - 1]], #[[n ;; 1 ;; -1]]], {n, Length[#]}] & [First[RealDigits[Pi, 10, 15]]] (* Paolo Xausa, Dec 08 2024 *)

A139258 Palindromes formed from the reflected decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.

Original entry on oeis.org

5, 55, 575, 5775, 57775, 577775, 5772775, 57722775, 577212775, 5772112775, 57721512775, 577215512775, 5772156512775, 57721566512775, 577215666512775, 5772156666512775, 57721566466512775, 577215664466512775

Offset: 1

Omar E. Pol, May 01 2008

			n ... Successive digits of a(n)
1 ............ ( 5 )
2 ......... . ( 5 5 )
3 .......... ( 5 7 5 )
4 ......... ( 5 7 7 5 )
5 ........ ( 5 7 7 7 5 )
6 ....... ( 5 7 7 7 7 5 )
7 ...... ( 5 7 7 2 7 7 5 )
8 ..... ( 5 7 7 2 2 7 7 5 )
9 .... ( 5 7 7 2 1 2 7 7 5 )
10 .. ( 5 7 7 2 1 1 2 7 7 5 )

Decimal expansion of gamma: A001620. Cf. A135634, A135697, A135700, A139259, A139260, A139261.

a[n_]:=FromDigits[Join[RealDigits[EulerGamma,10,Ceiling[n/2]][[1]],Reverse[RealDigits[EulerGamma,10,Floor[n/2]][[1]]]]];Array[a,18] (* James C. McMahon, Jun 29 2025 *)

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A138070 Triangle read by rows: row n lists the successive digits of A135697(n), the palindromic number formed from the reflected decimal expansion of Pi.

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A039954 Palindromic primes formed from the reflected decimal expansion of Pi.

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A135698 Palindromes with odd number of digits formed from the reflected decimal expansion of Pi.

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A138071 Triangle read by rows: row n lists the digits of A135698(n), the palindromic number with odd number of digits formed from the reflected decimal expansion of Pi.

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Mathematica

A139258 Palindromes formed from the reflected decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.

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