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.

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

1,1

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).

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Another version of A138840 which is older.

Cf. A000040, A007652, A010879.

Sequence in context: A171041 A094742 A110923 * A301378 A052424 A055398

Adjacent sequences: A137586 A137587 A137588 * A137590 A137591 A137592

Keyword

easy,base,nonn,look

Author

Ctibor O. Zizka, Apr 26 2008

Extensions

New name from Omar E. Pol, Mar 24 2018

Status

approved