A138840 Concatenation of initial and final digits of n-th prime.

22, 33, 55, 77, 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

Offset: 1

Author

Omar E. Pol, Apr 01 2008

Keywords

• base
• easy
• nonn
• look

Comments

There are only 38 distinct terms in this sequence, all of them odd with the exception of 22. 55 is the only term divisible by 5. 22 and 55 each appear only once. The other terms, each of which appears multiple times, are the odd two-digit numbers not divisible by 5. - Harvey P. Dale, May 15 2012

a(n) is the concatenation of A077648(n) and A007652(n), hence all terms of this sequence have two digits in the same way as A073729. - Omar E. Pol, Mar 23 2018

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Cf. A000040, A007652, A073729, A077648, A138841, A138842, A138843, A138844.

Cf. A137589 (same except for first four terms).

Programs

Maple

a:= n-> (p-> parse(cat(p[1], p[-1])))(""||(ithprime(n))):
seq(a(n), n=1..92);  # Alois P. Heinz, Nov 23 2023

Mathematica

cifd[n_]:=Module[{il=IntegerLength[n],idn=IntegerDigits[n]},Which[ il==1, 10n+n, il==2,n,il>2,FromDigits[Join[{First[idn],Last[idn]}]]]]; cifd/@ Prime[ Range[70]] (* Harvey P. Dale, May 15 2012 *)

PARI

a(n) = my(d=digits(prime(n))); fromdigits(concat(d[1], d[#d])); \\ Michel Marcus, Mar 23 2018