A139260 -id:A139260 - cp's OEIS frontend

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

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 *)

A139259 Triangle read by rows: row n lists the digits of A139258(n), the palindromic number formed from the reflected decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.

Original entry on oeis.org

5, 5, 5, 5, 7, 5, 5, 7, 7, 5, 5, 7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7, 2, 7, 7, 5, 5, 7, 7, 2, 2, 7, 7, 5, 5, 7, 7, 2, 1, 2, 7, 7, 5, 5, 7, 7, 2, 1, 1, 2, 7, 7, 5, 5, 7, 7, 2, 1, 5, 1, 2, 7, 7, 5, 5, 7, 7, 2, 1, 5, 5, 1, 2, 7, 7, 5

Offset: 1

Omar E. Pol, May 01 2008

Also, successive digits of A139258.

			Triangle begins:
....... 5
...... 5,5
..... 5,7,5
.... 5,7,7,5
... 5,7,7,7,5

Decimal expansion of gamma: A001620.

Cf. A138068, A138070, A138072, A139258, A139260, A139261.

a[n_]:=FromDigits[Join[RealDigits[EulerGamma,10,Ceiling[n/2]][[1]],Reverse[RealDigits[EulerGamma,10,Floor[n/2]][[1]]]]];IntegerDigits/@Array[a,12]//Flatten (* James C. McMahon, Jun 29 2025 *)

A139261 Triangle read by rows: row n lists the first n digits of the decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.

Original entry on oeis.org

5, 5, 7, 5, 7, 7, 5, 7, 7, 2, 5, 7, 7, 2, 1, 5, 7, 7, 2, 1, 5, 5, 7, 7, 2, 1, 5, 6, 5, 7, 7, 2, 1, 5, 6, 6, 5, 7, 7, 2, 1, 5, 6, 6, 4, 5, 7, 7, 2, 1, 5, 6, 6, 4, 9, 5, 7, 7, 2, 1, 5, 6, 6, 4, 9, 0, 5, 7, 7, 2, 1, 5, 6, 6, 4, 9, 0, 1

Offset: 1

Omar E. Pol, May 01 2008

Also, successive digits of A139260.

			Triangle begins:
....... 5
...... 5,7
..... 5,7,7
.... 5,7,7,2
... 5,7,7,2,1

Decimal expansion of gamma: A001620.

Cf. A138114, A138115, A138116, A139258, A139259, A139260.

a[n_]:=FromDigits[RealDigits[EulerGamma,10,n][[1]]];IntegerDigits/@Array[a,12]//Flatten (* James C. McMahon, Jun 29 2025 *)

A175835 Number of real roots of the polynomial Sum_{k=0..n-1} A001620(1+k-n)*x^k, whose coefficients are the decimal digits of the Euler-Mascheroni constant.

Original entry on oeis.org

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 3, 0, 3, 0, 3, 4, 1, 4, 1, 0, 1

Offset: 1

Michel Lagneau, Dec 05 2010

a(n) = number of real zeros of the polynomial P(n,x) = Sum_{k=0..n-1} g(k) x^k, where g(k) are the digits of the decimal expansion of floor(gamma*10^n), g(k)=A001620(k-n).

			a(4)=1 because 5772 = A139260(4) => P(4,x) = 2 + 7x + 7x^2 +  5x^3 has 1 real root near -0.4.

Cf. A173667, A001620.

A139260 := proc(n) floor(gamma*10^n) ;end proc:
A175835 := proc(n) local edgs ; edgs := convert(A139260(n),base,10) ; add(op(i,edgs)*x^(i-1),i=1..nops(edgs)) ; [fsolve(%,x,real)] ; nops(%) ; end proc:
seq(A175835(n),n=1..20) ; # R. J. Mathar, Dec 11 2010

cp's OEIS Frontend

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

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A139259 Triangle read by rows: row n lists the digits of A139258(n), the palindromic number formed from the reflected decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.

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A139261 Triangle read by rows: row n lists the first n digits of the decimal expansion of Euler's constant (or Euler-Mascheroni constant) gamma.

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A175835 Number of real roots of the polynomial Sum_{k=0..n-1} A001620(1+k-n)*x^k, whose coefficients are the decimal digits of the Euler-Mascheroni constant.

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