A223458 Primes whose first digit is a composite number.

41, 43, 47, 61, 67, 83, 89, 97, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881

Offset: 1

Author

K. D. Bajpai, Aug 24 2013

Keywords

• nonn
• base

Examples

			409 is a prime number whose first digit is 4, a composite number, so 409 is a term.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069090 (primes none of whose proper initial segments are primes).

Programs

Maple

KD := proc() local a,b,d,e;  a:= ithprime(n);  b:=length(a);  d:=a/(10^(b-1));  e:=floor(d); if isprime(e)=false and e>1 then RETURN (a): fi; end: seq(KD(),n=1..200);

Python

from sympy import primerange
from itertools import count, islice
def agen(): yield from (p for e in count(1) for k in [4, 6, 8, 9] for p in primerange(k*10**e, (k+1)*10**e))
print(list(islice(agen(), 54))) # Michael S. Branicky, Jun 25 2022