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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 (list; graph; refs; listen; history; text; internal format)
 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 Giovanni Resta, Table of n, a(n) for n = 1..10000 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 Adjacent sequences: A226096 A226097 A226098 * A226100 A226101 A226102 KEYWORD nonn,base,easy AUTHOR Jonathan Vos Post, May 26 2013 STATUS approved

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Last modified August 2 19:53 EDT 2024. Contains 374875 sequences. (Running on oeis4.)