A370848 - OEIS

A370848

Lesser of two consecutive primes such that the product of its digits is also prime and the sum of the digits of the other is composite.

13, 17, 31, 71, 113, 1151, 11131, 112111, 113111, 131111, 1111211, 1111711, 11111117, 11111171, 71111111, 115111111, 1111111121, 1111115111, 1115111111, 1117111111, 1151111111, 1711111111, 11111111113, 11113111111, 31111111111, 111113111111, 111511111111, 1111171111111

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OFFSET

1,1

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..3701

EXAMPLE

13 is a term because 13 is prime, the product of its digits is 3 which is also prime and the sum of the digits of 17, the next prime to 13, is 8 which is composite.

23 is not a term because the product of its digits is 6 which is not prime.

131 is not a term because although it is prime and the product of its digits is 3 which is also prime, the sum of the digits of 137, the next prime to 131, is 11 which is not composite.

MATHEMATICA

Select[Prime[Range[5*10^6]], PrimeQ[Apply[Times, IntegerDigits[#]]]&&CompositeQ[Total[IntegerDigits[NextPrime[#]]]]&] (* James C. McMahon, Mar 03 2024 *)

PROG

(PARI) isok(p)=my(x=vecprod(digits(p)), y=sumdigits(nextprime(p+1))); isprime(x) && !isprime(y);

forprime(p=2, 20000, if(isok(p), print1(p", ")))

(PARI) a370848(maxdigits=20) = {my (L=List()); for (n=2, maxdigits, my (r=(10^n-1)/9, d=digits(r)); foreach ([2, 3, 5, 7], s, for (k=1, #d, my (dd=d); dd[k]=s; my(q=fromdigits(dd)); if (ispseudoprime(q) && ! isprime(sumdigits(nextprime(q+1))), listput(L, q))))); vecsort(Vec(L))};

a370848() \\ Hugo Pfoertner, Mar 03 2024

(Python)

from itertools import count, islice

from sympy import isprime, nextprime

def A370848_gen(): # generator of terms

for l in count(1):

k = (10**l-1)//9

for m in range(l):

a = 10**m

for j in (1, 2, 4, 6):

p = k+a*j

if isprime(p) and not isprime(sum(map(int, str(nextprime(p))))):