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Positive integers that yield a prime when their most significant (i.e., leftmost) decimal digit is removed.
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%I #38 Sep 08 2022 08:46:05

%S 12,13,15,17,22,23,25,27,32,33,35,37,42,43,45,47,52,53,55,57,62,63,65,

%T 67,72,73,75,77,82,83,85,87,92,93,95,97,102,103,105,107,111,113,117,

%U 119,123,129,131,137,141,143,147,153,159,161,167,171,173,179,183,189,197,202,203,205,207,211,213,217

%N Positive integers that yield a prime when their most significant (i.e., leftmost) decimal digit is removed.

%C Terms < 110 are the same as in A260181, numbers whose last digit is prime. - _M. F. Hasler_, Dec 20 2019

%C These are numbers with decimal expansion of the form k = xp where p is a prime and x is a single digit. Whether or not the number k itself is a prime is irrelevant. - _N. J. A. Sloane_, Dec 21 2019

%H Giovanni Resta, <a href="/A226099/b226099.txt">Table of n, a(n) for n = 1..10000</a>

%F From _M. F. Hasler_, Dec 21 2019: (Start)

%F n in A226099 (this sequence) <=> A217657(n) in A000040 (prime).

%F a(n) = a(n-4) + 10 for 4 < n < 41, i.e., 20 < a(n) < 110; a(n) = a(n-25) for 61 < n < 287, i.e., 200 < a(n) < 1100, etc. (End)

%e a(1) = 12 because when its most significant (or leftmost) digit (1) is removed, the remaining number 2 is prime, and it is the least such number.

%e 102, 103, 105 and 107 are in the sequence because if the first digit is dropped, what is left is a 1-digit prime with a leading digit '0'.

%t Select[Range@ 300, PrimeQ@ FromDigits@ Rest@ IntegerDigits@ # &] (* _Giovanni Resta_, Dec 20 2019 *)

%o (PARI) select( is(n)=isprime(n%10^logint(n+!n,10)), [0..222]) \\ _M. F. Hasler_, Dec 20 2019

%o (Magma) [k:k in [1..220]| IsPrime( k-Reverse(Intseq(k))[1]*10^(#Intseq(k)-1 ))]; // _Marius A. Burtea_, Dec 21 2019

%Y Cf. A000040, A217657 (n without initial digit), A000030 (initial digit of n), A260181 (last digit is prime), A202262 (substrings are composite).

%K nonn,base,easy

%O 1,1

%A _Jonathan Vos Post_, May 26 2013