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A136296 "Special augmented primes": primes p such that the decimal number 1p1 is divisible by p.

%I A136296 #34 Jan 27 2025 21:11:20
%S A136296 11,13,137,9091,909091,5882353,909090909090909091,
%T A136296 909090909090909090909090909091,
%U A136296 9090909090909090909090909090909090909090909090909091,909090909090909090909090909090909090909090909090909090909090909091
%N A136296 "Special augmented primes": primes p such that the decimal number 1p1 is divisible by p.
%C A136296 Equals A116436 INTERSECT A000040. - _R. J. Mathar_, Apr 24 2008
%C A136296 The larger terms may be only probable primes. - _Franklin T. Adams-Watters_, Apr 23 2008
%C A136296 According to the Magma Calculator (http://magma.maths.usyd.edu.au/calc/), all nine terms given for this sequence are prime. - _Jon E. Schoenfield_, Aug 24 2009
%D A136296 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61.
%H A136296 Michael S. Branicky, <a href="/A136296/b136296.txt">Table of n, a(n) for n = 1..12</a> (all terms with <= 1000 digits)
%e A136296 11371/137 = 83, an integer, so the prime 137 is a term.
%t A136296 max=6; a={}; For[i=1, i<=10^max, i++, If[Mod[FromDigits[Join[{1}, IntegerDigits[Prime[i]], {1}]], Prime[i]] == 0, AppendTo[a, Prime[i]]]]; a (* _Stefano Spezia_, Mar 26 2023 *)
%o A136296 (PARI)
%o A136296 A136296k(k) = { local(l, d, lb, ub); d=factor(10^(k+1)+1)[,1]; l=[]; lb=10^(k-1); ub=10*lb; for(i=1,#d,if(d[i]>=lb&&d[i]<ub,l=concat(l,[d[i]]))); l}
%o A136296 concat(vector(60, k, A136296k(k))) \\ _Franklin T. Adams-Watters_, Apr 23 2008
%o A136296 (Python)
%o A136296 from sympy import isprime
%o A136296 from itertools import count, islice
%o A136296 def agen(): # generator of terms
%o A136296     for k in count(2):
%o A136296         t = 10**(k+1) + 1
%o A136296         d = [t//i for i in range(100, 10, -1) if t%i == 0]
%o A136296         yield from (di for di in d if isprime(di))
%o A136296 print(list(islice(agen(), 8))) # _Michael S. Branicky_, Mar 26 2023 following _Franklin T. Adams-Watters_ but removing factorization
%Y A136296 Prime members of A116436.
%K A136296 nonn,base
%O A136296 1,1
%A A136296 _N. J. A. Sloane_, Apr 20 2008
%E A136296 a(4)-a(6) from _M. F. Hasler_, Apr 22 2008
%E A136296 a(7)-a(9) from _Franklin T. Adams-Watters_, Apr 23 2008
%E A136296 a(10) from _Michael S. Branicky_, Mar 26 2023