

A359113


a(n) counts the bases b in the interval 2 to p = prime(n), where p if written in base b gives again a prime number in base b if all digits are written in reverse order.


1



0, 1, 3, 5, 7, 10, 12, 9, 14, 15, 20, 19, 23, 26, 24, 33, 22, 30, 38, 36, 40, 39, 38, 33, 54, 49, 43, 52, 37, 60, 65, 53, 59, 57, 50, 52, 85, 52, 79, 76, 57, 77, 69, 103, 90, 83, 84, 106, 80, 68, 90, 85, 89, 94, 75, 100, 108, 87, 128, 97, 119, 99, 118, 139, 105, 96
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OFFSET

1,3


COMMENTS

Let p' be p with digit reversal in base b. If p' is composite then all multiplication operations c * d = p' in base b of integers c,d > 1 are using carry in long multiplication. For A000040(n) this is the case in A000040(n)  (a(n)+1) bases.
Prime indices of numbers in A228768 are also among the indices of the records in the rational number sequence a(n)/(n1) with n > 1. See also the plot of this sequence in the link section.


LINKS



FORMULA



EXAMPLE

a(3) = 3:
prime(3) = 5 in bases 2..5:
5 = 101_2; reversing digits gives 101_2 = 5 (prime).
5 = 12_3; reversing digits gives 21_3 = 7 (prime).
5 = 11_4; reversing digits gives 11_4 = 5 (prime).
5 = 10_5; reversing digits gives 01_5 = 1 (nonprime).


PROG

(PARI) revprime(p, b)=my(q, t=p); while(t, q=b*q+t%b; t\=b); isprime(q)
a(n) = sum(b = 2, prime(n), revprime(prime(n), b))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



