A301378 a(n) = 10*A007605(n) - 9*A007652(n).

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, 23, 37, 41, 47, 49, 59, 61, 67, 73, 77, 83, 89, 91, 101, 103, 107, 109, 31, 43, 47, 49, 53, 59, 61, 71, 77, 83, 89, 91, 97, 101, 103, 113, 37, 41, 43, 47, 61

Offset: 1

Author

Edmund Algeo, Mar 19 2018

Keywords

• nonn
• easy
• base
• less

Comments

Equivalently, a(n) is the sum of all but the last digit of the n-th prime, concatenated with that last digit.

It appears that as the prime number xyzd transformed by (x+y+z)*10 +d; the larger the prime the less frequent the result is prime....

Examples

			For p=1571 (prime), 1+5+7 = 13; 13*10 = 130; 130+1 = 131 (prime).
		

Links

• Shawn A. Broyles, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007605, A007652, A176044.

Programs

Maple

map(t -> 10*convert(convert(t,base,10),`+`)-9*(t mod 10), [seq(ithprime(i),i=1..100)]); # Robert Israel, Mar 25 2018

Mathematica

Array[10 Total@ # - 9 Last@ # &@ IntegerDigits[Prime@ #] &, 67] (* Michael De Vlieger, Apr 27 2018 *)

PARI

a(n) = my(p=prime(n); d=p % 10); sumdigits(p-d)*10+d; \\ Michel Marcus, Mar 23 2018

Formula

Let ...xyzd represent the decimal expansion of prime(n); then a(n) = (... + x + y + z)*10 + d.

a(n) = 10*A007605(n) - 9*A007652(n). - Robert Israel, Mar 25 2018