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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A280419 Primes in A132934.

Original entry on oeis.org

1468910121415161820212224252627283032333435363839, 14689101214151618202122242526272830323334353638394042444546484950515254555657586062636465666869
Offset: 1

Views

Author

Sergey Pavlov, Jan 02 2017

Keywords

Comments

Primes that can be obtained from concatenation of the nonprime numbers.
In other words: primes that can be obtained from concatenation of 1 and the next consecutive composite numbers.
For a(n), the smallest prime divisor is a(n) and a(n) is a term of A241845.

Crossrefs

A241845 a(1)=1; for n >1 a(n) is the smallest prime divisor of the number obtained from concatenation of 1 and the first n-1 composites.

Original entry on oeis.org

1, 2, 2, 2, 37, 2, 2, 2, 5, 2, 2, 2, 27793, 2, 2, 3, 2, 29, 2, 2, 2, 19, 2, 5, 2, 2, 1468910121415161820212224252627283032333435363839, 2, 2, 2, 5, 2, 2, 3, 2, 127, 2, 2, 5, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2
Offset: 1

Views

Author

Paolo P. Lava, Apr 30 2014

Keywords

Comments

a(1)=1, and for n > 1 a(n) is the smallest prime divisor of the number obtained from the concatenation of A018252(j), j=1, ..., n. - Wolfdieter Lang, May 07 2014

Examples

			1 U 4 = 14 and its divisors are 1, 2, 7, 14. Then a(2) = 2.
14 U 6 = 146 and its divisors are 1, 2, 73, 146. Then a(3) = 2.
146 U 8 = 1468 and its divisors are 1, 2, 4, 734, 367, 1468. Then a(4) = 2.
1468 U 9 = 14689 and its divisors are 1, 37, 397, 14689. Then a(5) = 37. Etc.
		

Crossrefs

Programs

  • Maple
    with(numtheory):
    T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
    P:=proc(q) local a,b,n; b:=1; print(1); for n from 2 to q do if not isprime(n) then b:=n+b*10^T(n); a:=sort([op(divisors(b))]); print(a[2]);
    fi; od; end: P(10^6); # Paolo P. Lava, Apr 30 2014
  • Mathematica
    Module[{nn=70,cmps},cmps=Select[Range[nn],CompositeQ];Join[ {1},SelectFirst[ Divisors[#],PrimeQ]&/@FromDigits/@Table[ Join[ {1},Flatten[ IntegerDigits/@Take[cmps,n]]],{n,Length[cmps]}]]] (* Harvey P. Dale, Jul 27 2021 *)

Extensions

More terms from Jinyuan Wang, Jun 27 2020
Showing 1-2 of 2 results.