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 1-3 of 3 results.

A376002 Positions of records in A032662.

Original entry on oeis.org

1, 3, 5, 22, 84, 99, 511, 803, 9999, 18887, 1378751, 103974046
Offset: 1

Views

Author

Robert Israel, Sep 05 2024

Keywords

Comments

Numbers k such that the first j for which the concatenation j || j+k is prime is greater than for any previous k.
In order for j || j+k to be prime where j+k has d digits, k and 10^d+1 must be coprime.

Examples

			a(5) = 84 because A032662(84) = 929 which is greater than A032662(k) for all k < 84.

Crossrefs

Cf. A032662, A376006.

Programs

  • Maple
    tcat:= (a,b) -> a*10^(1+ilog10(b))+b:
f:= proc(n) local k,k0,d;
  for d from ilog10(n)+1 do
    if igcd(10^d+1,n) = 1 then
      k0:= max(1,10^(d-1)-n);
      if (k0+n)::even then k0:= k0+1 fi;
      for k from k0 to 10^d-n-1 by 2 do
        if isprime(tcat(k,k+n)) then return k fi
   od fi od
end proc:
R:= NULL: m:= 0: count:= 0:
for i from 1 while count < 11 do
  v:= f(i);
  if v > m then
    count:= count+1; m:= v; R:= R,i;
  fi;
od:
R;

A376006 Record values in A032662.

Original entry on oeis.org

2, 4, 12, 21, 929, 938, 9500, 99204, 9990074, 99999981142, 999999998621256, 99999999999999896026031
Offset: 1

Views

Author

Robert Israel, Sep 05 2024

Keywords

Comments

a(n) is the least k for which the concatenation k || k + A376002(n) is prime.

Examples

			a(5) = 929 because A376002(5) = 84 and A032662(84) = 929.  Thus 84 + 929 = 1013, the concatenation 9291013 is prime, the concatenations k || k+84 are composite for 1 <= k < 929, and for every m < 84 there is k < 929 where k || k+m is prime.

Crossrefs

Cf. A032662, A376002.

Programs

  • Maple
    tcat:= (a, b) -> a*10^(1+ilog10(b))+b:
f:= proc(n) local k, k0, d;
  for d from ilog10(n)+1 do
    if igcd(10^d+1, n) = 1 then
      k0:= max(1, 10^(d-1)-n);
      if (k0+n)::even then k0:= k0+1 fi;
      for k from k0 to 10^d-n-1 by 2 do
        if isprime(tcat(k, k+n)) then return k fi
   od fi od
end proc:
V:= NULL: m:= 0: count:= 0:
for i from 1 while count < 11 do
  v:= f(i);
  if v > m then
    count:= count+1; m:= v; V:= V, v;
  fi;
od:
V;

Formula

a(n) = A032662(A376002(n)).

A032663 Primes that are the smallest decimal concatenations of n with n + (0,1,2,3,...).

Original entry on oeis.org

11, 23, 13, 47, 37, 1217, 17, 29, 19, 211, 313, 617, 113, 619, 317, 419, 521, 421, 523, 827, 727, 223, 2143, 1033, 1741, 227, 127, 229, 331, 433, 131, 233, 739, 1447, 337, 439, 137, 239, 139, 241, 1151, 647, 547, 1861, 347, 449, 349, 653, 149, 251, 151, 859
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Comments

First terms of sequences '11', A030458, A032625-A032632,continued with displacements d > 9.

Examples

			6th term is prime 1217: 17 - 12 = displacement 5 (=6-1).

Crossrefs

Cf. A032662.

Extensions

Edited by Charles R Greathouse IV, Apr 30 2010
Showing 1-3 of 3 results.

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

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