cp's OEIS Frontend

A167416 Smallest prime concatenation of the first n primes, or 0 if no such prime exists.

%I A167416 #27 Dec 05 2021 05:38:03
%S A167416 2,23,523,2357,112573,11132357,1113257317,111317193257,11131719223357,
%T A167416 0,111317192232935317,11131719223293157373,1113171922329313377541,
%U A167416 111317192232931337415743,11131719223293133741474357
%N A167416 Smallest prime concatenation of the first n primes, or 0 if no such prime exists.
%C A167416 a(10) doesn't exist, because the sum of digits of the first 10 primes (2+3+5+7+(1+1)+(1+3)+(1+7)+(1+9)+(2+3)+(2+9)) = 57 is a multiple of 3.
%D A167416 Richard E. Crandall and Carl Pomerance, Prime Numbers, Springer 2005.
%D A167416 Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996.
%D A167416 A. Weil, Number theory: an approach through history, Birkhäuser 1984.
%e A167416 The only prime concatenations of the first n primes for n = 1..3 are a(1)=2, a(2)=23, and a(3)=523.
%e A167416 For n=4, the only prime concatenations of 2, 3, 5, and 7 are 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523; the smallest of these is a(4) = 2357.
%o A167416 (Python)
%o A167416 from sympy import sieve, isprime
%o A167416 from itertools import permutations
%o A167416 for n in range(1, 20):
%o A167416     sieve.extend_to_no(n)
%o A167416     p = list(map(str, list(sieve._list)))[:n]
%o A167416     mint = 10**1000
%o A167416     for i in permutations(p, len(p)):
%o A167416         t = int(''.join(i))
%o A167416         if  t < mint and isprime(t):
%o A167416             mint = t
%o A167416     if mint == 10**1000:
%o A167416         print(0, end = ', ')
%o A167416     else:
%o A167416         print(mint, end = ', ') # _Gleb Ivanov_, Dec 04 2021
%Y A167416 Cf. A175429, A177275, A134966, A167417.
%K A167416 nonn,base
%O A167416 1,1
%A A167416 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 03 2009
%E A167416 Keyword:full added by _R. J. Mathar_, Nov 11 2009
%E A167416 Edited by _Charles R Greathouse IV_, Apr 28 2010
%E A167416 Several terms corrected and a(11)-a(15) from _Gleb Ivanov_, Dec 04 2021