A074830 Number of base reversals which result in a prime for bases less than n.

0, 0, 1, 0, 3, 2, 5, 2, 1, 3, 7, 3, 10, 4, 3, 3, 12, 4, 9, 5, 4, 7, 14, 4, 11, 5, 5, 7, 15, 3, 20, 9, 6, 6, 12, 3, 19, 11, 9, 6, 23, 4, 26, 8, 6, 10, 24, 7, 17, 11, 7, 15, 33, 4, 19, 9, 12, 12, 22, 5, 30, 16, 11, 13, 15, 4, 38, 15, 14, 8, 36, 5, 40, 17, 7, 13, 32, 4, 39, 13, 6, 13, 38, 4, 25

Offset

1,5

Comments

If n is composite, then there does not exist any base greater than n whose base reversal is prime. And if n is a prime, then there exist an infinite number of bases greater than n whose base reversals are primes (hence this sequence's restriction to bases up to n only).

Links

Table of n, a(n) for n=1..85.

Example

a(5) = 3 because 5 = 101_2 and its reversal 101_2 = 5, 5 = 12_3 and its reversal 21_3 = 7, 5 = 11_4 and its reversal 11_4 = 5. 3, 7, and 5 are all primes.

Mathematica

a[n_] := Block[{c = 0, b = 2}, While[b < n + 1, If[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[n, b]], b]], c++ ]; b++ ]; c]; Table[ a[n], {n, 1, 85}]

Prog

(PARI) a(n) = sum(b=2, n-1, isprime(fromdigits(Vecrev(digits(n, b)), b))); \\ Michel Marcus, Apr 29 2021

Crossrefs

Sequence in context: A093527 A088233 A056008 * A369043 A182983 A231146

Adjacent sequences: A074827 A074828 A074829 * A074831 A074832 A074833

Keyword

base,easy,nonn

Author

Robert G. Wilson v, Sep 09 2002

Status

approved