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.

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A074809 Largest prime factor of A019518, concatenation of first n primes.

Original entry on oeis.org

2, 23, 47, 2357, 223, 35339, 214282847, 7717859, 806801, 185176472401, 357211, 4967701595369, 104364752351, 27558919, 5269410931806332951, 274784055330749, 1191126125288819, 178258515898000387, 2313161253378144566969023310693, 8730041915527145606449758346652473, 26293517701186435480644832888393, 29890227360205834316383307128051, 3858432486690092813, 7122852423207105431971, 93753283248830261744671
Offset: 1

Views

Author

Jason Earls, Sep 08 2002

Keywords

Examples

			For n=5: concatenation of {2,3,5,7,11} is 235711 = 7*151*223, largest prime divisor is a(5)=223.

Links

Crossrefs

Cf. A019518.

Programs

  • Mathematica
    <Labos Elemer, Mar 18 2005 *)
Table[FactorInteger[FromDigits[Flatten[IntegerDigits/@Prime[ Range[n]]]]][[-1,1]],{n,25}] (* Harvey P. Dale, Apr 27 2015 *)
  • PARI
    a(n) = vecmax(factor(eval(concat(apply(s->Str(s), primes(n)))))[,1]); \\ Daniel Suteu, May 26 2022

Formula

a(n) = A006530(A019518(n)). - Daniel Suteu, May 26 2022

Extensions

More terms from Labos Elemer, Mar 18 2005
Edited by Charles R Greathouse IV, Apr 23 2010

A191248 The number of times that the n-th digit of A019518(n) occurs in A019518(n).

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 4, 2, 5, 2, 6, 2, 3, 6, 3, 2, 7, 8, 7, 6, 3, 9, 3, 9, 3, 9, 3, 10, 3, 7, 2, 19, 2, 12, 12, 24, 13, 15, 14, 9, 2, 16, 3, 12, 13, 17, 38, 4, 38, 38, 4, 21, 39, 4, 19, 40, 4, 18, 41, 42, 23, 42, 23, 23, 45, 29, 47, 47, 34, 26, 47, 38, 21, 47, 7
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 28 2011

Keywords

Links

Crossrefs

Cf. A019518, A191233.

Programs

  • Maple
    with(StringTools): lim:=100: s:="": for j from 1 to lim do s:=cat(s, convert(ithprime(j),string)): printf("%d, ", nops([SearchAll(s[j], s)])); od: # Nathaniel Johnston, May 28 2011

Extensions

Corrected and extended by Nathaniel Johnston, May 28 2011

A185695 Final prime adjoined in the smallest term of A019518 divisible by 61^n.

Original entry on oeis.org

23, 41719, 308537, 270907253, 28643801327
Offset: 1

Views

Author

James G. Merickel, Feb 05 2011

Keywords

Comments

Associated with A019518(i) at i = 9, 4363, 26688, 14758114, ...

Crossrefs

Cf. A019518, A185656, A185659, A185662, A185665, A185671, A185677.

Programs

  • Python
    from sympy import nextprime
def A185695(n):
    p, k, m = 2, 61**n, 10
    q, m2 = p % k, m % k
    while True:
        p = nextprime(p)
        while p >= m:
            m *= 10
            m2 = m % k
        q = (q*m2 + p) % k
        if q == 0:
            return p # Chai Wah Wu, May 01 2020

Extensions

a(5) from Chai Wah Wu, May 01 2020

A185698 Final prime adjoined in the smallest term of A019518 divisible by 67^n.

Original entry on oeis.org

37, 37, 14123267, 47321411, 5664619381
Offset: 1

Views

Author

James G. Merickel, Feb 05 2011

Keywords

Comments

Associated with A019518(i) at i = 12, 12, 917579, 2849864, ...

Examples

			23571113171923293137 is divisible by 67^2.

Crossrefs

Cf. A019518, A185656, A185659, A185662, A185665, A185671, A185677.

Programs

  • Python
    from sympy import nextprime
def A185698(n):
    p, k, m = 2, 67**n, 10
    q, m2 = p % k, m % k
    while True:
        p = nextprime(p)
        while p >= m:
            m *= 10
            m2 = m % k
        q = (q*m2 + p) % k
        if q == 0:
            return p # Chai Wah Wu, May 01 2020

Extensions

a(5) from Chai Wah Wu, May 01 2020

A238593 Smallest m such that the n-th prime occurs as substring in A019518(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 2, 10, 7, 12, 13, 14, 15, 16, 17, 18, 19, 5, 21, 22, 23, 24, 25, 26, 27, 28, 29, 6, 31, 7, 12, 34, 35, 36, 37, 38, 19, 21, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 32, 59, 60, 61, 11, 63, 33, 12, 7, 66, 68
Offset: 1

Views

Author

Reinhard Zumkeller, Mar 03 2014

Keywords

Comments

a(n) <= n; see A165450 for earley bird primes: A165450(n) = A000040(m) with a(m) < m.

Examples

			n=10, prime(10)=29 occurs first in A019518(10)=2357111317192329, therefore a(10) = 10;
prime(11)=31 occurs already in A019518(7)=2357111317, therefore a(11) = 7.

Links

Programs

  • Haskell
    import Data.List (isInfixOf, findIndex); import Data.Maybe (fromJust)
a238593 n = (+ 1) $ fromJust $ findIndex
   (isInfixOf $ show $ a000040 n) (scanl1 (++) $ map show a000040_list)

A104645 Difference between the previous and the next primes to x, where x is the number obtained from concatenation of the first n primes (A019518).

Original entry on oeis.org

10, 6, 20, 24, 24, 60, 18, 48, 100, 48, 156, 74, 88, 68, 42, 126, 366, 106, 186, 136, 228, 104, 30, 246, 52, 218, 814, 58, 536, 174, 90, 924, 180, 298, 120, 330, 96, 508, 504, 60, 762, 588, 330, 138, 552, 726, 452, 634, 660, 354, 534, 1770, 52, 262, 834, 790, 250, 624
Offset: 2

Views

Author

Labos Elemer, Mar 18 2005

Keywords

Examples

			For n=4, concatenate(2,3,5,7) gives 2357. The closest other primes are 2371 and 2351 and their difference is a(4)=20.

Crossrefs

Cf. A019518, A074809, A104462, A104463.

Programs

Formula

a(n) = A151800(A019518(n)) - A151799(A019518(n)).

Extensions

Corrected, extended, and edited by Charles R Greathouse IV, Apr 28 2010

A185668 Final prime of first member of A019518 that is divisible by 19^n.

Original entry on oeis.org

271, 1831, 66947, 3746299, 66478091, 66478091, 57260418041
Offset: 1

Views

Author

James G. Merickel, Feb 01 2011

Keywords

Examples

			The first concatenation of primes--23, 235, 2357, 235711, etc.--that is divisible by 19 concatenates through 271, and to get divisibility by 19^2 it's necessary to go through 1831.

Crossrefs

Cf. A183194, A185656, and those following.

A185674 Final prime added in the smallest term of A019518 divisible by 29^n.

Original entry on oeis.org

13, 4783, 251513, 17958713, 244826371, 19062911531
Offset: 1

Views

Author

James G. Merickel, Feb 05 2011

Keywords

Comments

Associated with A019518(i) at i = 6, 642, 22164, 1148866, 13411613, ...

Examples

			23571113 is divisible by 29, but it's necessary to concatenate through 4783 to get a number divisible by 29^2.

Crossrefs

Cf. A019518, A185656, A185659, A185662, A185665, A185671, A185677, A009973.

A185683 Final prime adjoined in the smallest term of A019518 divisible by 41^n.

Original entry on oeis.org

439, 439, 922457, 24105901, 2278313963, 9480709177
Offset: 1

Views

Author

James G. Merickel, Feb 05 2011

Keywords

Comments

Associated with A019518(i) at i = 85, 85, 72914, 1513350,...

Crossrefs

Cf. A185656, A185659, A185662, A185665, A185671, A185671, A185680.

A185686 Final prime adjoined in the smallest term of A019518 divisible by 47^n.

Original entry on oeis.org

5, 15149, 186191, 21897151, 14431069151
Offset: 1

Views

Author

James G. Merickel, Feb 05 2011

Keywords

Comments

Associated with A019518(i) at i = 3, 1770, 16855, 1383135,...

Crossrefs

Cf. A009991, A185656, A185659, A185662, A185665, A185671, A185677, A185680.
Previous Showing 11-20 of 84 results. Next

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