A088628 -id:A088628 - cp's OEIS frontend

A069599 Duplicate of A088628.

11, 127, 1123, 1423, 112543, 1124653, 1234657, 112345687, 1234156789, 10124356789

Offset: 1

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A069600 Smallest square containing all the digits of numbers from 1 to n. For a(10) and higher, all duplicated digits must be in the term (for example a(10) has two 1's).

1, 121, 3721, 13924, 135424, 1236544, 13527684, 13527684, 139854276, 11738205649, 10112819764356, 1011123678945241, 10118426359171321, 10111134329645378121, 1011111632116847554329, 10111124953183456116721, 1011111119736855441726321, 101111112641746351915327881, 10111111111271587168434259369

Offset: 1

Amarnath Murthy, Mar 25 2002

			a(5) = 335241 = 579^2 contains digits 1,2,3,4 and 5.

Cf. A088628.

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jan 20 2003
a(14)-a(15) from Giovanni Resta, Aug 06 2019
a(16)-a(19) from Chai Wah Wu, May 18 2020

A069601 Smallest triangular number containing all the digits of numbers from 1 to n.

Original entry on oeis.org

1, 21, 231, 12403, 24531, 235641, 2467531, 13862745, 153694278, 10429651378, 1017139458621, 101114872391625, 10111496127133528, 1011137441915312286, 101111293764315411825, 10111111491815764232356, 1011111155214617733491628, 101111111617874325294116835

Offset: 1

Amarnath Murthy, Mar 25 2002

For a(10) and higher, all duplicated digits must be in the term (for example a(10) has two 1's).

Conjecture: except for a(4), the digits of a(n) are exactly all the digits of numbers from 1 to n. - Chai Wah Wu, May 18 2020

			a(5) = 219453 = T(662) contains digits 1, 2, 3, 4 and 5.

Chai Wah Wu, Table of n, a(n) for n = 1..29

Cf. A088628, A069600.

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jan 24 2003

a(15)-a(18) from Chai Wah Wu, May 18 2020

A332265 a(n) is the number of prime numbers created when concatenating all the arrangements of the decimal integers from 0 to 3*n+4.

Original entry on oeis.org

20, 3202, 2056675, 3500185228

Offset: 0

Scott R. Shannon, May 04 2020

Only 4 and every third integer after 4 can create primes when concatenating the integer arrangements of 0,...,3*n+4 as the other integer values will create numbers with digit sums divisible by 3, and hence are divisible by 3. The digit 0 is allowed to be the first digit in the number but is then ignored when determining if the remaining digits form a prime.

			a(0) = 20 as there are twenty primes created when concatenating the integer arrangements of 0,1,2,3,4. They are 1423, 2143, 2341, 4231, 10243, 12043, 20143, 20341, 20431, 23041, 24103, 30241, 32401, 40123, 40213, 40231, 41023, 41203, 42013, 43201.
a(1) = 3202. The smallest prime created using integers 0..7 is 1234657 while the largest is 76540231.
a(2) = 2056675. The smallest prime created using integers 0..10 is 10123457689 while the largest is 987654310021.

Cf. A000040, A295206, A006879, A050288, A088628, A185122, A176009, A099182.

Table[Count[FromDigits /@  Flatten /@ IntegerDigits /@ Permutations[Range[0, 3 n + 4]], ?PrimeQ], {n, 0, 2}] (* _Robert Price, Sep 16 2020 *)
(* OR, if the above runs low on memory to store all the Permutations at once... *)
Table[p0 = Range[0, 3n+4]; p = NextPermutation[p0]; c = 0;
 While[p != p0,
  If[PrimeQ[FromDigits[Flatten[IntegerDigits /@ p]]], c++];
p = NextPermutation[p]]; c, {n, 0, 2}] (* Robert Price, Sep 16 2020 *)

a(3) from Giovanni Resta, May 04 2020

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A069599 Duplicate of A088628.

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A069600 Smallest square containing all the digits of numbers from 1 to n. For a(10) and higher, all duplicated digits must be in the term (for example a(10) has two 1's).

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A069601 Smallest triangular number containing all the digits of numbers from 1 to n.

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A332265 a(n) is the number of prime numbers created when concatenating all the arrangements of the decimal integers from 0 to 3*n+4.

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