A090269 - OEIS

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A090269

Least k made of identical digits such that the concatenation k, prime(n), k is prime. a(5) = 0.

7, 1, 1, 3, 0, 33, 1, 9, 1, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 7, 3, 3, 1, 1111, 111, 3, 3, 1, 9, 1, 33, 1, 111, 3, 1, 3, 3, 9, 777, 1, 3, 77, 7, 9, 1, 777, 9, 3, 7, 333, 7, 1, 3, 1, 3, 3, 3, 3, 9, 7, 3, 3, 3, 3, 9, 1, 9, 777, 7, 3, 3, 1, 77, 9, 11, 1, 3, 9, 1, 9

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..80.

MAPLE

isA010785 := proc(n) convert(convert(n, base, 10), set) ; if nops(%) = 1 then true ; else false ; fi ; end: A055642 := proc(n) ilog10(n)+ 1; end: A090269 := proc(n) local kern, k, p ; if n = 5 then RETURN(0) ; fi ; kern := ithprime(n) ; k := 1 ; while true do if isA010785(k) then p := k+10^A055642(k)*kern+k*10^(A055642(k)+A055642(kern)) ; if isprime(p) then RETURN(k) ; fi ; fi ; k := k+1 ; od ; end: seq(A090269(n), n=1..80); # R. J. Mathar, Jul 20 2007

PROG

(Python)

from sympy import prime, isprime

def a(n):

if n == 5: return 0

spn, digits = str(prime(n)), 1

while True:

for sk in [d*digits for d in "1379"]:

if isprime(int(sk + spn + sk)): return int(sk)

digits += 1

print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Jul 01 2021

CROSSREFS