A137589 - OEIS

%I #25 Mar 27 2018 17:21:01

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,11,13,17,19,13,17,11,17,19,19,11,17,13,17,13,19,11,11,13,17,19,21,

%U 23,27,29,23,29,21,21,27,23,29,21,27,21,23,23,37,31,33,37,31,37,37,39,33

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

%C 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).

%H David A. Corneth, <a href="/A137589/b137589.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A138840(n) if n >= 5. - _Omar E. Pol_, Mar 23 2018

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

%t 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 *)

%o (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

%Y Another version of A138840 which is older.

%Y Cf. A000040, A007652, A010879.

%K easy,base,nonn,look

%O 1,1

%A _Ctibor O. Zizka_, Apr 26 2008

%E New name from _Omar E. Pol_, Mar 24 2018