A191291 -id:A191291 - cp's OEIS frontend

A191322 Number of bases in which both n and the reversal of n are 3-digit numbers.

0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 0, 0, 1, 2, 2, 2, 3, 2, 2, 2, 0, 0, 1, 2, 3, 3, 2, 2, 2, 3, 0, 1, 2, 2, 3, 4, 2, 3, 3, 3, 0, 1, 2, 3, 2, 2, 4, 4, 4, 4, 0, 0, 1, 2, 2, 1, 4, 4, 4, 4, 0, 0, 1

Offset: 1

Vladimir Shevelev, May 30 2011

			a(36)=3 since 36 is 3-digit number in bases 4,5,6 and 63 is 3-digit number in bases 4,5,6,7 such that we have 3 common bases.

Cf. A002113, A191291.

a(n) = a(inv(n)).
a(A002113(n)) = A191291(A002113(n)).
a(n) <= min(A191291(n),A191291(inv(n))).

A191350 The number of bases not exceeding n+1 in which the expansion of n (i) has only digits <=9 and (ii) represents a prime if digits are concatenated/reinterpreted as decimals.

Original entry on oeis.org

1, 2, 1, 3, 1, 3, 2, 2, 3, 3, 2, 4, 2, 4, 4, 5, 3, 7, 4, 6, 6, 8, 4, 7, 5, 6, 6, 8, 4, 9, 4, 9, 7, 7, 4, 11, 5, 9, 6, 8, 4, 13, 4, 8, 7, 10, 5, 10, 5, 8, 7, 9, 4, 14, 5, 8, 8, 11, 4, 12, 4, 10, 8, 8, 5, 15, 6, 8, 6, 13, 4, 14, 5, 10, 6, 8, 6, 17, 5, 8, 7, 12, 6, 13, 5, 11, 8, 11, 4, 15, 5

Offset: 2

Vladimir Shevelev, May 31 2011

			In bases 6, 8, 12 and 14 the digits of n=15 are 15_6=23, 15_8=17, 15_12=13, and 15_14=11. Since in other bases<=16 the expansions of 15 converted to decimal are not primes, a(15)=4.

Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Cf. A191291, A191322.

a(n)=my(m,t,k,i);sum(b=2,n+1,k=n;m=0;i=0;while(k,t=k%b;if(t>9,m=0;break);m+=10^i*t;i++;k\=b);isprime(m)) \\ Charles R Greathouse IV, Jun 01 2011

a(16)-a(91) from Charles R Greathouse IV, Jun 01 2011

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A191322 Number of bases in which both n and the reversal of n are 3-digit numbers.

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A191350 The number of bases not exceeding n+1 in which the expansion of n (i) has only digits <=9 and (ii) represents a prime if digits are concatenated/reinterpreted as decimals.

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