cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A138843 Concatenation of initial and final digits of n-th perfect number.

Original entry on oeis.org

66, 28, 46, 88, 36, 86, 18, 28, 26, 16, 18, 18, 26, 18, 58, 18, 96, 36, 16, 48, 16, 56, 36, 96, 16, 86, 36, 18, 18, 16, 28, 18, 86, 88, 36, 16, 86, 96, 46
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, concatenation of A135617(n) and A094540(n).

Examples

			a(5)=36 because the 5th perfect number A000396(5) is 33550336 and the concatenation of initial and final digits of 33550336 is 36.

Crossrefs

Cf. A000396, A073729, A135617, A094540, A138840, A138841, A138842, A138844.

A138841 Concatenation of initial and final digit of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 31, 17, 81, 11, 57, 27, 21, 61, 17, 17, 61, 57, 17, 17, 41, 21, 11, 27, 41, 31, 21, 41, 41, 41, 81, 57, 57, 51, 77, 17, 11, 47, 81, 61, 11, 41, 91, 17, 27, 17, 31, 11, 27, 11, 31
Offset: 1

Views

Author

Omar E. Pol, Apr 01 2008

Keywords

Examples

			a(5)=81 because the 5th Mersenne prime is 8191, A000668(5)=8191.

Crossrefs

Cf. A000668, A073729, A080172, A135613, A138840, A138842, A138843.

Formula

a(n) = A073729(A000668(n)). - Michel Marcus, Apr 17 2018

Extensions

a(40)-a(47) from Ivan Panchenko, Apr 17 2018

A138842 Concatenation of initial and final digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

22, 44, 16, 64, 46, 66, 24, 14, 16, 36, 84, 84, 36, 24, 54, 74, 26, 16, 96, 14, 26, 16, 16, 26, 26, 26, 46, 24, 24, 26, 34, 84, 66, 24, 46, 36, 66, 26, 46, 64, 14, 64, 16, 66, 14, 86, 16
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, concatenation of initial and final digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.
Also, concatenation of A138124(n) and A138125(n).

Crossrefs

Cf. A019279, A061652, A073729, A138124, A138125, A138838, A138840, A138841, A138843, A138844.

Extensions

More terms from Jinyuan Wang, Mar 14 2020

A138866 Concatenation of first 3 digits and last 3 digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 3131, 127127, 819191, 131071, 524287, 214647, 230951, 618111, 162127, 170727, 686151, 531127, 104087, 147007, 446351, 259071, 190991, 285607, 478111, 346551, 281191, 431471, 448751, 402511, 854671, 536207, 521007, 512311, 746447, 174887, 129591, 412527, 814711, 623151, 127271, 437791, 924071, 125047, 299407, 122247, 315871, 124871, 202927, 169751, 316511
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

Crossrefs

Cf. A000668, A080173, A104511, A138816, A138817, A138840, A138841.

Programs

  • Mathematica
    Join[{33,77,3131},FromDigits[Flatten[Join[{Take[IntegerDigits[#],3],Take[ IntegerDigits[ #],-3]}]]]&/@ (2^MersennePrimeExponent[Range[4,40]]-1)] (* Harvey P. Dale, Dec 30 2023 *)

Extensions

More terms from Harvey P. Dale, Dec 30 2023

A138844 Concatenation of initial and final digits of n-th positive Fibonacci number.

Original entry on oeis.org

11, 11, 22, 33, 55, 88, 13, 21, 34, 55, 89, 14, 23, 37, 60, 97, 17, 24, 41, 65, 16, 11, 27, 48, 75, 13, 18, 31, 59, 80, 19, 29, 38, 57, 95, 12, 27, 39, 66, 15, 11, 26, 47, 73, 10, 13, 23, 46, 79, 15, 24, 39, 53, 82, 15, 27, 32, 59, 91, 10, 21, 41, 62, 13, 15, 28, 43, 71, 14
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Comments

Also, concatenation of A008963(n) and A003893(n).

Examples

			a(15) = 60 because the 15th positive Fibonacci number is 610 and the concatenation of initial and final digits of 610 is 60.

Links

Crossrefs

Cf. A000045, A003893, A008963, A073729, A138840, A138841, A138842, A138843.

Programs

  • Maple
    a:= n-> (f-> parse(cat(f[1], f[-1])))(""||(combinat[fibonacci](n))):
seq(a(n), n=1..92);  # Alois P. Heinz, Nov 23 2023
  • Mathematica
    FromDigits[Join[{IntegerDigits[#][[1]]},{IntegerDigits[#][[-1]]}]]&/@ Fibonacci[Range[70]] (* Harvey P. Dale, Jun 15 2018 *)

A138863 Concatenation of first two digits and last two digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 3131, 1227, 8191, 1371, 5287, 2147, 2351, 6111, 1627, 1727, 6851, 5327, 1087, 1407, 4451, 2571, 1991, 2807, 4711, 3451, 2891, 4371, 4451, 4011, 8571, 5307, 5207, 5111, 7447, 1787, 1291, 4127, 8111, 6251, 1271, 4391, 9271, 1247, 2907, 1247, 3171, 1271, 2027, 1651, 3111
Offset: 1

Views

Author

Omar E. Pol, Apr 02 2008

Keywords

Links

Crossrefs

Cf. A000668, A080173, A104511, A138816, A138817, A138840, A138841, A138862, A138864, A138865, A138866.

Extensions

More terms from Jinyuan Wang, Mar 14 2020

A137589 a(n) is the integer that results after deletion of all digits of n-th prime, except the initial digit and the final digit.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 11, 13, 17, 19, 13, 17, 11, 17, 19, 19, 11, 17, 13, 17, 13, 19, 11, 11, 13, 17, 19, 21, 23, 27, 29, 23, 29, 21, 21, 27, 23, 29, 21, 27, 21, 23, 23, 37, 31, 33, 37, 31, 37, 37, 39, 33
Offset: 1

Views

Author

Ctibor O. Zizka, Apr 26 2008

Keywords

Comments

The plot of this sequence shows number of primes on the x-axis and the split of primes into 9 groups according to their first digit on the y-axis. The plot of a(n+1)/a(n) oscillates around 1 with decreasing amplitude. Log-periodic growth is seen on the plot of partial sums b(n)= Sum_(i=1..n) a(i).

Examples

			a(100) = 51 as prime(100) = 541. Concatenating the first and last digit gives 51. - _David A. Corneth_, Mar 23 2018

Links

Crossrefs

Another version of A138840 which is older.
Cf. A000040, A007652, A010879.

Programs

  • Mathematica
    fdld[n_]:=Module[{idn=IntegerDigits[n]},FromDigits[{First[idn], Last[ idn]}]]; Join[Prime[Range[25]],fdld/@Prime[Range[26,100]]] (* Harvey P. Dale, Oct 10 2012 *)
  • PARI
    a(n) = my(p = prime(n), d); if(n<=4, return(p)); d = digits(p); 10*d[1] + d[#d] \\ David A. Corneth, Mar 23 2018

Formula

a(n) = A138840(n) if n >= 5. - Omar E. Pol, Mar 23 2018

Extensions

New name from Omar E. Pol, Mar 24 2018
Showing 1-7 of 7 results.

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