A383781 Primes where successively deleting the most significant digit yields a sequence that alternates between a prime and a nonprime at every step until a single-digit number remains.
2, 3, 5, 7, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 127, 157, 163, 193, 227, 233, 257, 263, 277, 293, 433, 457, 463, 487, 557, 563, 577, 587, 593, 677, 727, 733, 757, 787, 827, 857, 863, 877, 887, 977, 1129, 1171, 1231, 1259, 1279, 1289, 1319, 1361, 1429, 1459
Offset: 1
Examples
127 is a term since 127 is a prime, 27 is a nonprime, and 7 is a prime; 13 is not a term since 13 and 3 are both prime.
Programs
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Mathematica
Unprotect[CompositeQ]; CompositeQ[1]:=True; Protect[CompositeQ]; Q[n_]:=And[AllTrue[FromDigits/@Table[Take[IntegerDigits[n], -i], {i,IntegerLength[n],1,-2}], PrimeQ], AllTrue[FromDigits/@Table[Take[IntegerDigits[n], -i], {i,IntegerLength[n]-1,1,-2}], CompositeQ]]; Select[Prime[Range[240]], Q] -
Python
from gmpy2 import is_prime, mpz from itertools import count, islice def agen(): olst, elst = [2, 3, 5, 7], [11, 19, 29, 31, 41, 59, 61, 71, 79, 89] for n in count(1): yield from sorted(olst + elst) olst2, elst2 = [], [] for o in olst: o, base = o, 10**(2*n-1) for i in range(10*base, 100*base, base): t = i + o t2 = int(str(t)[1:]) if is_prime(t) and not is_prime(t2): olst2.append(t) for e in elst: e, base = e, 10**(2*n) for i in range(10*base, 100*base, base): t = i + e t2 = int(str(t)[1:]) if is_prime(t) and not is_prime(t2): elst2.append(t) olst, elst = olst2, elst2 print(list(islice(agen(), 68))) # Michael S. Branicky, May 11 2025
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