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A226099
Positive integers that yield a prime when their most significant (i.e., leftmost) decimal digit is removed.
4
12, 13, 15, 17, 22, 23, 25, 27, 32, 33, 35, 37, 42, 43, 45, 47, 52, 53, 55, 57, 62, 63, 65, 67, 72, 73, 75, 77, 82, 83, 85, 87, 92, 93, 95, 97, 102, 103, 105, 107, 111, 113, 117, 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
OFFSET
1,1
COMMENTS
Terms < 110 are the same as in A260181, numbers whose last digit is prime. - M. F. Hasler, Dec 20 2019
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
LINKS
FORMULA
From M. F. Hasler, Dec 21 2019: (Start)
n in A226099 (this sequence) <=> A217657(n) in A000040 (prime).
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)
EXAMPLE
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.
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'.
MATHEMATICA
Select[Range@ 300, PrimeQ@ FromDigits@ Rest@ IntegerDigits@ # &] (* Giovanni Resta, Dec 20 2019 *)
PROG
(PARI) select( is(n)=isprime(n%10^logint(n+!n, 10)), [0..222]) \\ M. F. Hasler, Dec 20 2019
(Magma) [k:k in [1..220]| IsPrime( k-Reverse(Intseq(k))[1]*10^(#Intseq(k)-1 ))]; // Marius A. Burtea, Dec 21 2019
CROSSREFS
Cf. A000040, A217657 (n without initial digit), A000030 (initial digit of n), A260181 (last digit is prime), A202262 (substrings are composite).
Sequence in context: A175225 A187234 A127354 * A179512 A125664 A262210
KEYWORD
nonn,base,easy
AUTHOR
Jonathan Vos Post, May 26 2013
STATUS
approved