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A268031
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Primes with the property that deleting some two digits one at a time in unique order gives a prime (with an even number of digits) at each step, until the empty string is reached.
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0
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11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 1009, 1021, 1049, 1051, 1063, 1069, 1087, 1201, 1409, 1609, 1663, 1669, 1801, 2003, 2011, 2017, 2063, 2069, 2267, 2609, 2621, 2657, 2663, 2687, 2767, 2861, 3001, 3023
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The prime 2657 is in the sequence because the set {57, 67, 65, 27, 25, 26} contains only one two-digit prime.
The prime 1021 is in the sequence because the set {21, 1, 2, 11, 12, 10} contains only one prime with an even number of digits.
The prime 1579 is not in the sequence because the set {79, 59, 57, 19, 17, 15} contains four two-digit primes.
The number 2087 is not in the sequence because the set {87, 7, 8, 27, 28, 20} does not contain any prime with an even number of digits.
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PROG
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(Magma) /* generates first 211 terms */; lst:=[m: m in [11..99 by 2] | IsPrime(m)]; for m in [1001..9999 by 2] do if IsPrime(m) then S:=[]; Temp:=Intseq(m); for a in [2..4] do for b in [1..a-1] do d:=Seqint([Temp[b], Temp[a]]); if IsPrime(d) and d gt 10 then Append(~S, d); end if; end for; end for; if #S eq 1 then Append(~lst, m); end if; end if; end for; lst; // Arkadiusz Wesolowski, Dec 17 2020
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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