A268031 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.
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
Offset: 1
Examples
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.
Links
- Chris Caldwell, The Prime Glossary, Deletable prime
Programs
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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