A226217 Primes whose first digit is a square.
11, 13, 17, 19, 41, 43, 47, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 907, 911, 919, 929, 937, 941, 947, 953
Offset: 1
Examples
97 is a prime whose first digit is 9, which is 3^2, so 97 is a term.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A223458 (similar sequence for primes: first digit a composite number).
Programs
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Maple
KD := proc() local a,b,d,e; a:= ithprime(n); b:=length(a); d:=a/(10^(b-1)); e:=floor(d); if evalf(sqrt(e))=floor(evalf(sqrt(e))) then RETURN (a):fi;end:seq(KD(),n=1..200);
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Mathematica
Select[Prime[Range[200]],MemberQ[{1,4,9},First[IntegerDigits[#]]]&] (* Harvey P. Dale, Sep 02 2023 *) -
Python
from sympy import primerange from itertools import count, islice def agen(): yield from (p for e in count(1) for k in [1, 4, 9] for p in primerange(k*10**e, (k+1)*10**e)) print(list(islice(agen(), 54))) # Michael S. Branicky, Jun 25 2022