A075242 -id:A075242 - cp's OEIS frontend

A075241 Least base for which the n-th prime has no prime reversal in that base.

2, 3, 5, 7, 4, 6, 3, 2, 6, 3, 7, 4, 4, 3, 4, 5, 2, 7, 10, 3, 3, 2, 6, 2, 3, 6, 2, 3, 2, 4, 4, 4, 2, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 10, 3, 3, 2, 3, 4, 3, 9, 2, 2, 3, 3, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 3, 2, 4, 6, 4, 2, 3, 2, 3, 2, 2, 2, 5, 2, 4, 4, 3, 2, 3, 6, 2, 3, 4, 2, 3, 3, 6, 2, 4, 3, 4, 2, 2, 2, 2, 2

Offset: 1

Robert G. Wilson v, Sep 09 2002

a(n) is always less than or equal to n-th prime and once past a(6) it is always less than n.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A075240, A075242.

a = {}; Do[k = 2; p = Prime[n]; While[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[p, k]], k]], k++ ]; a = Append[a, k], {n, 1, 105}]; a

A075240 Smallest prime whose base-n reversal is not a prime.

Original entry on oeis.org

2, 3, 11, 5, 13, 7, 11, 29, 19, 11, 19, 13, 29, 23, 19, 17, 23, 19, 31, 29, 29, 23, 29, 37, 37, 29, 31, 29, 43, 31, 37, 37, 59, 59, 43, 37, 41, 59, 43, 41, 59, 43, 47, 47, 53, 47, 59, 61, 59, 61, 59, 53, 67, 59, 59, 59, 61, 59, 73, 61, 71, 67, 79, 71, 89, 67, 71, 101, 89

Offset: 2

Robert G. Wilson v, Sep 09 2002

All primes show up in the sequence eventually.

			11_10 = 23_4, reverse(23) = 32, 32_4 = 14_10, so a(4) = 11 since this does not work for smaller primes.

Amiram Eldar, Table of n, a(n) for n = 2..10000

Cf. A075241, A075242.

a = {}; Do[k = 1; While[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[ Prime[k], n]], n]], k++ ]; a = Append[a, Prime[k]], {n, 2, 70}]; a

a(n) = my(p=2); while (isprime(fromdigits(Vecrev(digits(p, n)), n)), p = nextprime(p+1)); p; \\ Michel Marcus, Mar 28 2021

A075243 Composite numbers requiring increasingly larger bases to become prime by base reversal.

Original entry on oeis.org

4, 6, 8, 9, 16, 27, 36, 78, 81, 102, 114, 144, 270, 420, 480, 750, 1848, 2382, 2940, 13860, 14490, 14520, 21840, 31860, 33660, 44580, 80850, 1228080, 4305210, 5326860, 6846840, 9796710, 9990750, 10720710, 14910630, 15129510, 15278250, 16785090, 17022390, 17608500

Offset: 1

Robert G. Wilson v, Sep 09 2002

The bases at which these entries occur are in A074901. See A075242.

Amiram Eldar, Table of n, a(n) for n = 1..48

Cf. A074901, A075242.

NextComposite[n_] := Block[{k = n + 1}, While[PrimeQ[k], k++ ]; k]; f[n_] := Block[{b = 2}, While[b < n && !PrimeQ[ FromDigits[ Reverse[ IntegerDigits[n, b]], b]], b++ ]; b]; If[b != n, b, 0]; b = -1; k = 4; Do[ While[c = f[k]; c <= b, k = NextComposite[k]]; b = c; Print[k], {n, 1, 31}]

More terms from Amiram Eldar, Jun 04 2021

A075244 Least number requiring the base n to produce a prime by base reversal.

Original entry on oeis.org

2, 3, 15, 8, 109, 9, 119, 16, 27, 70, 2197, 36, 1265, 158, 213, 178, 4205, 126, 14189, 260, 273, 304, 4865, 120, 1295, 78, 81, 532, 44323, 150, 47317, 952, 771, 102, 16705, 492, 6209, 114, 1209, 2020, 132743, 294, 22945, 2834, 2721, 2276, 66455, 144

Offset: 1

Robert G. Wilson v, Sep 09 2002

Question, Is every base necessary to convert the natural numbers into primes?

			a(1) = 2 because two = 11 in unary (A000042) and its reversal 11 = 2. a(2) = 3 because three = 11 in base 2 (A007088) and its reversal 11 in base 2 = 3. a(3) = 15 because fifteen = 120 in base 3 (A007089) and its reversal 21 in base 3 = 7. a(4) = 8 -> 2. a(7) = 119 because 119 base 7 = 230 in base 7 (A007093) and its reversal 32 base 7 = 161.

Cf. A075241 & A075242.

f[n_] := Block[{b = 2}, While[b < n && !PrimeQ[ FromDigits[ Reverse[ IntegerDigits[n, b]], b]], b++ ]; If[b != n, b, 0]]; a = Table[0, {70}]; Do[b = f[n]; If[b < 76 && a[[b]] == 0, a[[b]] = n], {n, 2, 133000}]

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A075241 Least base for which the n-th prime has no prime reversal in that base.

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A075240 Smallest prime whose base-n reversal is not a prime.

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A075243 Composite numbers requiring increasingly larger bases to become prime by base reversal.

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Extensions

A075244 Least number requiring the base n to produce a prime by base reversal.

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