cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A342836 a(n) is the smallest prime factor of A342834(n).

Original entry on oeis.org

7, 797, 3, 7, 37, 3023681, 43, 1249, 7, 3, 23, 11, 3, 19, 3, 13390093693131976661567, 193, 2069, 11, 41, 3, 71, 3, 996370591, 3, 101, 1123, 54367, 159469, 151, 29, 3, 7
Offset: 1

Views

Author

Bernard Schott, Mar 24 2021

Keywords

Comments

a(n) = A342834(n) for n = 1 and n = 2, no other solution is known.
No primes through a(258). - Michael S. Branicky, Mar 25 2021
a(34) <= 7944676315964871787139677901. a(35)..a(40) = 2089, 11, 3, 23, 3, 11. a(42)=3. - Chai Wah Wu, Mar 26 2021

Examples

			As A342834(5) = 7||97||997||9973||99991 = 797997997399991 = 37 * 951649 * 22663307, then a(5) = 37.

Links

Crossrefs

Cf. A020639, A338968, A342834, A342835.

Formula

a(n) = A020639(A342834(n)).

Extensions

a(4)-a(14) from Daniel Suteu, Mar 24 2021
a(15)-a(33) from Michael S. Branicky and Apurva Rai, Mar 25 2021

A342835 a(n) is the number of divisors of A342834(n).

Original entry on oeis.org

2, 2, 8, 16, 8, 4, 64, 4, 32, 8, 128, 64, 16, 64, 512, 8, 8, 64, 64
Offset: 1

Views

Author

Bernard Schott, Mar 23 2021

Keywords

Comments

a(21) = 96, a(63) = 4. - Chai Wah Wu, Mar 26 2021

Examples

			a(1) = a(2) = 2 because A342834(1) = 7 and A342834(2) = 797 are primes.
a(4) = 16 because A342834(4) = 7979979973 = 7 * 23 * 137 * 361789.

Crossrefs

Cf. A000005, A342834, A342836.

Formula

a(n) = A000005(A342834(n)).

Extensions

a(3)-a(11) from Michel Marcus, Mar 23 2021
a(12)-a(14) from Daniel Suteu, Mar 23 2021
a(15)-a(18) from Michael S. Branicky and Apurva Rai, Mar 26 2021
a(19) from Sean A. Irvine, May 01 2023

A342837 Starting with A342834(n), a(n) is the number of n-digit primes we have to go back from A003618(n) through the sequence of these n-digit primes to get the prime A338968(n).

Original entry on oeis.org

0, 0, 3, 3, 16, 40, 8, 44, 112, 85, 48, 24, 168, 15, 182, 18, 13, 151, 348, 204, 437, 612, 771, 75, 51, 310, 796, 111, 811, 350, 644, 350, 469, 159, 571, 544, 2239, 4, 1474, 97, 2177, 175, 1400, 1791, 75, 1983, 337, 2503, 854, 2397, 830, 246, 5350, 1682, 153, 1581, 622
Offset: 1

Views

Author

Bernard Schott, Mar 29 2021

Keywords

Comments

The idea of this sequence comes from Daniel Suteu.
A338968(n) is the concatenation of A342834(n-1) with the largest n-digit prime p <= A003618(n) such that A342834(n-1)||p is prime where || stands for concatenation.
Both A338968(n) and A342834(n) have n*(n+1)/2 digits.

Examples

			For a(2), as A338968(2) = A342834(2) = 7||97 = 797, a(2) = 0.
From _Daniel Suteu_, Mar 29 2021: (Start)
For a(3), as A003618(1) = 7, A003618(2) = 97 and A003618(3) = 997, we have A342834(3) = 7||97||997 = 797997 while prime A338968(3) = 7||97||977 = 797977.
# 7||97||997 = 797997 = 3 * 17 * 15647 is not prime (#1 fail)
# 7||97||991 = 797991 = 3 * 461 * 577 is not prime (#2 fail)
# 7||97||983 = 797983 = 41 * 19463 is not prime (#3 fail)
# 7||97||977 = 797977 = A338968(3) is prime.
Therefore, the largest 3-digit prime p <= 997 such that A342834(2)||p is prime, is p = 977. Through the sequence of the 3-digit primes, we have to go back 3 primes from A003618(3) = 997 (991, 983, 977) in order to get A338968(3), hence a(3) = 3. (End)

Crossrefs

Cf. A003618, A338968, A342834.

Formula

a(n) = primepi(A003618(n)) - primepi(A338968(n) mod 10^n). - David A. Corneth, Mar 29 2021

Extensions

a(3)-a(57) from Daniel Suteu, Mar 29 2021

A342838 Indices m such that A342834(m) is not squarefree.

Original entry on oeis.org

21, 31, 32, 39, 42, 62, 67, 75, 82, 91, 93, 97, 104, 109, 121, 127, 135, 137, 139, 140, 145, 146
Offset: 1

Views

Author

Bernard Schott and Daniel Suteu, Apr 01 2021

Keywords

Comments

From the factorization of the initial terms of A342834, it may appear that A342834(n) is always squarefree, but this is false, and that present sequence lists the exceptions.

Crossrefs

Cf. A013929, A342834, A342835, A342836, A342837.

Programs

  • PARI
    f(n) = my(s=""); for (k=1, n, s = Str(s, precprime(10^k))); eval(s); \\ A342834
isok(m) = !issquarefree(f(m)); \\ Michel Marcus, Apr 01 2021
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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