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

Author

Ctibor O. Zizka, Apr 26 2008

Keywords

• easy
• base
• nonn
• look

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

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

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