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 A195302 Xmas tree primes. 3
 2, 3, 5, 7, 211, 223, 229, 241, 271, 283, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 523, 541, 547, 571, 719, 743, 761, 773, 797, 211151, 211193, 211199, 211229, 211241, 211271, 211283, 211313, 211349, 211373, 211433, 211457, 211499, 211571, 211619, 211643, 211661, 211691, 211727, 211811, 211859, 211877, 211997, 213131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A Xmas tree prime is a prime which is a concatenation of a prime with a single digit, a prime with two digits, a prime with three digits, a prime with four digits etc. By definition, the number of digits is a triangular number (A000217). Leading zeros are not allowed for any of the primes. LINKS Alvin Hoover Belt, Table of n, a(n) for n = 1..100 Terry Trotter, POTPOURRI [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018] EXAMPLE 359 is a Xmas tree prime because it is prime and 3 and 59 are prime. 503 is not a Xmas tree prime although 5 and 3 are prime, because the leading 0 in front of the 3 is not allowed by definition. MAPLE isA000217 := proc(n)         for k from 0 do                 if n = k*(k+1)/2 then                         return k;                 elif n < k*(k+1)/2 then                         return -1 ;                 end if;         end do; end proc: isA195302 := proc(n)         local dgs, T, d, std, kList, k ;         if isprime(n) then                 dgs := convert(n, base, 10) ;                 T := isA000217(nops(dgs)) ;                 if T > 0 then                         std := 1 ;                         for d from T to 1 by -1 do                                 kList := [op(std..std+d-1, dgs)] ;                                 if op(-1, kList) = 0 then                                         return false;                                 end if;                                 k := add(op(i, kList)*10^(i-1), i=1..nops(kList)) ;                                 if not isprime(k) then                                         return false;                                 end if;                                 std := std+d ;                         end do:                         return true;                 else                         false;                 end if;         else                 false;         end if; end proc: for i from 2 to 300000 do         if isA195302(i) then                 printf("%d, ", i) ;         end if; end do: # R. J. Mathar, Sep 20 2011 PROG (Python) from sympy import isprime, sieve from itertools import product def alst(n):   alst, plen = [], 1   while True:     sieve.extend(10**plen-1)     primes = list(str(p) for p in sieve._list)     primesbylen = [[p for p in primes if len(p)==i+1] for i in range(plen)]     for t in product(*primesbylen):       intt = int("".join(t))       if isprime(intt): alst.append(intt)       if len(alst) == n: return alst     plen += 1 print(alst(57)) # Michael S. Branicky, Dec 26 2020 CROSSREFS Cf. A195335. Sequence in context: A029978 A122764 A256886 * A064157 A257483 A178371 Adjacent sequences:  A195299 A195300 A195301 * A195303 A195304 A195305 KEYWORD nonn,base AUTHOR Kausthub Gudipati, Sep 16 2011 STATUS approved

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Last modified June 22 12:52 EDT 2021. Contains 345380 sequences. (Running on oeis4.)