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

11, 13, 137, 9091, 909091, 5882353, 909090909090909091, 909090909090909090909090909091, 9090909090909090909090909090909090909090909090909091, 909090909090909090909090909090909090909090909090909090909090909091

Offset

1,1

Comments

Equals A116436 INTERSECT A000040. - R. J. Mathar, Apr 24 2008

The larger terms may be only probable primes. - Franklin T. Adams-Watters, Apr 23 2008

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

References

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..12 (all terms with <= 1000 digits)

Example

11371/137 = 83, an integer, so the prime 137 is a term.

Mathematica

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 *)

Prog

(PARI) 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} l=[]; for(i=1, 60, l=concat(l, A136296k(i))); l \\ Franklin T. Adams-Watters, Apr 23 2008
(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    for k in count(2):
        t = 10**(k+1) + 1
        d = [t//i for i in range(100, 10, -1) if t%i == 0]
        yield from (di for di in d if isprime(di))
print(list(islice(agen(), 8))) # Michael S. Branicky, Mar 26 2023 following Franklin T. Adams-Watters but removing factorization

Crossrefs

Prime members of A116436.

Sequence in context: A276694 A086549 A108090 * A094621 A178426 A252170

Adjacent sequences: A136293 A136294 A136295 * A136297 A136298 A136299

Keyword

nonn,base

Author

N. J. A. Sloane, Apr 20 2008

Extensions

a(4)-a(6) from M. F. Hasler, Apr 22 2008

a(7)-a(9) from Franklin T. Adams-Watters, Apr 23 2008

a(10) from Michael S. Branicky, Mar 26 2023

Status

approved