

A214342


Count of the decimal descendants of the nth prime.


3



23, 22, 11, 23, 1, 14, 4, 40, 15, 6, 7, 13, 1, 14, 5, 0, 9, 16, 11, 4, 15, 1, 1, 0, 3, 10, 28, 0, 12, 0, 8, 1, 1, 9, 5, 1, 4, 1, 0, 2, 0, 6, 2, 5, 10, 19, 3, 5, 5, 6, 8, 5, 7, 0, 5, 3, 5, 8, 4, 1, 2, 5, 1, 2, 2, 0, 9, 5, 0, 7, 7, 2, 11, 9, 2, 2, 0, 0, 4, 28, 0, 7
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OFFSET

1,1


COMMENTS

Prime q is a decimal descendant of prime p if q = p*10+k and 0<=k<=9.
The number of direct decimal descendants is A038800(p).
a(n) is the total count of direct decimal descendants of the nth prime that are also prime, plus their decimal descendants that are prime, and so on.
Conjecture: no terms bigger than 35 after a(8)=40.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


EXAMPLE

prime(3)=5 has eleven descendants: 53, 59, 593, 599, 5939, 59393, 59399, 593933, 593993, 5939333, 59393339. So a(3)=11. All candidates of the form 5nnn1 and 5nnn7 are divisible by 3.
prime(5)=11, the only decimal descendant of 11 that is prime is 113, and because there are no primes between 1130 and 1140, a(5)=1.


MAPLE

A214342 := proc(n)
option remember;
local a, p, k, d ;
a := 0 ;
p := ithprime(n) ;
for k from 0 to 9 do
d := 10*p+k ;
if isprime(d) then
a := a+1+procname(numtheory[pi](d)) ;
end if;
end do:
return a;
end proc: # R. J. Mathar, Jul 19 2012


MATHEMATICA

Table[t = {Prime[n]}; cnt = 0; While[t = Select[Flatten[Table[10*i + {1, 3, 7, 9}, {i, t}]], PrimeQ]; t != {}, cnt = cnt + Length[t]]; cnt, {n, 100}] (* T. D. Noe, Jul 24 2012 *)


CROSSREFS

Cf. A214280, A055781, A055782, A055783, A055784.
Sequence in context: A077146 A077576 A004512 * A261308 A022979 A023465
Adjacent sequences: A214339 A214340 A214341 * A214343 A214344 A214345


KEYWORD

nonn,base


AUTHOR

Alex Ratushnyak, Jul 12 2012


STATUS

approved



