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 1-2 of 2 results.

A120805 Primes with consecutive digits.

Original entry on oeis.org

2, 3, 5, 7, 23, 43, 67, 89, 109, 4567, 10987, 76543, 78901, 678901, 23456789, 45678901, 9012345678901, 789012345678901, 56789012345678901234567890123, 90123456789012345678901234567, 10987654321098765432109876543210987
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits can be in ascending or descending order. After 9 comes 0 or after 0 comes 1.
The number of primes with n consecutive digits: 4,4,1,1,3,1,0,2,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,...,.

Crossrefs

Cf. A000040, A118697; union of A006055 & A120804.

Programs

  • Mathematica
    f[n_] := Block[{u = Range@n, d = Reverse@ Range@n, t = Table[1, {n}]}, Select[ Drop[ Union@ Flatten@ Table[ FromDigits /@ Mod[{u, d} + {i*t, i*t}, 10], {i, 10}], 2], PrimeQ@# &]]; Array[f, 35] // Flatten

A215477 Semiprimes with consecutive (ascending) digits.

Original entry on oeis.org

4, 6, 9, 34, 123, 789, 901, 1234, 34567, 56789, 901234, 1234567, 7890123, 567890123, 12345678901, 345678901234567, 4567890123456789, 12345678901234567, 890123456789012345, 3456789012345678901, 456789012345678901234, 123456789012345678901234567, 1234567890123456789012345678901, 23456789012345678901234567890123
Offset: 1

Views

Author

Jonathan Vos Post, Aug 12 2012

Keywords

Comments

This is to semiprimes A001358 as A006055 is to primes.

Examples

			a(9) = 34567 because it is semiprime 13 * 2659, and (3,4,5,6,7) are consecutive ascending digits.
		

Crossrefs

Programs

  • Maple
    R:= 4, 6, 9: V:= [$1..9]:
    for d from 2 to 50 do
    V:= map(n -> 10*n + ((n+1) mod 10), V);
    W:= select(t -> numtheory:-bigomega(t)=2, V);
    R:= R, op(W);
    od:
    R; # Robert Israel, Nov 15 2023

Extensions

Corrected and extended by R. J. Mathar, Aug 13 2012
Showing 1-2 of 2 results.