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.
Original entry on oeis.org
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
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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/* 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
A350443
Rigidly-deletable primes: primes such that removing some digit, one at a time in unique order gives a prime at each step, until the empty string is reached.
Original entry on oeis.org
2, 3, 5, 7, 13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 127, 157, 163, 269, 271, 359, 383, 439, 457, 463, 487, 509, 547, 569, 571, 643, 659, 683, 701, 709, 751, 769, 863, 929, 983, 1217, 1427, 1487, 2069, 2371, 2609, 2671, 2689, 2713, 2731, 2791, 2969, 3259
Offset: 1
The prime 103 is not a member since removing a digit will either give 03 which has a leading zero (3 is a prime number), or give one of the numbers 13 which is prime, or 10 which is composite.
The prime 509 is a member since removing a digit will either give 09 which has a leading zero (9 is a composite number), or give one of the numbers 59 which is prime, or 50 which is composite. Then removing a digit from 59 will either give 9, or 5 which is prime.
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for(k=2, 3259, if(isprime(k), a=k; r=#digits(a); q=r; for(y=1, r, L=List([]); for(d=1, q, T=List(Vec(Str(a))); listpop(T, d); listput(L, concat(T))); t=0; for(b=1, q, w=L[b]; if(isprime(eval(w)), t++; u=w); if(t==2, break)); if(t==1, q=#Vec(u); a=u, break); if(y==r, print1(k, ", ")))));
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from sympy import isprime
def ok(n):
if not isprime(n): return False
if n < 10: return True
s, c, d = str(n), 0, None
for i in range(len(s)):
di = int(s[:i]+s[i+1:])
if isprime(di):
c += 1
if c > 1:
return False
d = di
return d and ok(d) and len(str(d)) == len(s) - 1
print([k for k in range(3260) if ok(k)]) # Michael S. Branicky, Dec 31 2021
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