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 1-5 of 5 results.

A069557 Squares in which the k-th significant digit either divides k or is a multiple of k. Is 1 only in case k has no other single-digit divisor.

Original entry on oeis.org

1, 4, 9, 25, 49, 64, 81, 324, 361, 625, 961, 4624, 8649, 7354944
Offset: 1

Views

Author

Amarnath Murthy, Mar 22 2002

Keywords

Comments

If the smallest prime divisor of n is > 7 only in such case the n-th digit is 1.
a(15) > 10^25 if it exists. - David A. Corneth, May 05 2024
The definition implies that no digit can be zero. - N. J. A. Sloane, May 05 2024

Examples

			8649 is a member in which the fourth digit is 8, a multiple of 4, the third one is 6, a multiple of 3, the second one is 4, a multiple of 2 and the least significant digit is 9.

Links

Crossrefs

Cf. A052041, A069556, A069560.

Programs

  • Mathematica
    okQ[n_]:=Module[{idn=IntegerDigits[n]}, Count[idn,0]==0 && And@@Divisible[idn,Range[Length[idn],1,-1]]]; Select[Range[500]^2, okQ]  (* Harvey P. Dale, Dec 20 2010 *)
  • PARI
    \\ See PARI link

Extensions

More terms from Sascha Kurz, Mar 23 2002
Offset corrected and a(14) from Sean A. Irvine, May 04 2024

A069558 Triangular numbers in which the k-th digit, numbering them from right to left, either divides k or is a nonzero multiple of k. Is 1 only when k has no other single-digit divisor (less than 10).

Original entry on oeis.org

1, 3, 6, 21, 28, 45, 66, 325, 666, 946, 2346, 2628, 2926, 8385, 8646, 52326, 54946
Offset: 1

Views

Author

Amarnath Murthy, Mar 22 2002

Keywords

Comments

The n-th digit is 1 only when the smallest prime divisor of n is > 7.
Next term > 10^18. - Sascha Kurz, Mar 23 2002

Examples

			8646 is a term in which, numbering the digits from right to left,
the 1st digit is 6;
the 2nd digit is 4, a multiple of 2;
the 3rd digit is 6, a multiple of 3;
the 4th digit is 8, a multiple of 4.

Crossrefs

Cf. A000217, A069556, A069557, A069559.

Extensions

Offset corrected by Sean A. Irvine, May 04 2024

A069559 Triangular numbers in which the k-th significant digit either divides k or is a multiple of k.

Original entry on oeis.org

1, 3, 6, 15, 21, 28, 45, 66, 325, 666, 946, 1128, 1326, 2145, 2346, 2628, 2926, 4186, 8128, 8385, 8646, 8911, 11325, 11628, 14365, 18145, 18915, 51681, 52326, 54615, 54946, 58311, 111628, 118341, 152628, 214185, 258121, 614386, 1152921, 1211346
Offset: 1

Views

Author

Amarnath Murthy, Mar 22 2002

Keywords

Comments

If the smallest prime divisor of n is > 7 then the n-th digit is 1.

Examples

			8646 is a member in which the fourth digit is 8 a multiple of 4, the third one is 6 a multiple of 3, the second one is 4 a multiple of 2 and the least significant digit is 6.

Crossrefs

Intersection of A000217 and A069570.
Cf. A069556, A069557, A069558.

Extensions

More terms from Sascha Kurz, Mar 23 2002
Offset changed by Andrew Howroyd, Sep 19 2024

A069560 Squares in which the k-th significant digit either divides k or is a multiple of k.

Original entry on oeis.org

1, 4, 9, 16, 25, 49, 64, 81, 121, 144, 169, 324, 361, 625, 961, 1369, 1681, 2116, 2916, 4624, 8649, 11664, 12321, 14161, 14641, 51984, 114921, 151321, 214369, 311364, 351649, 1151329, 1252161, 1658944, 7311616, 7354944, 41254929, 41654116
Offset: 1

Views

Author

Amarnath Murthy, Mar 22 2002

Keywords

Comments

If the smallest prime divisor of n is > 7 then the n-th digit is 1.
a(65) if it exists is > 10^50. - Andrew Howroyd, Sep 20 2024

Examples

			8649 is a member in which the fourth digit is 8 a multiple of 4, the third one is 6 a multiple of 3, the second one is 4 a multiple of 2 and the least significant digit is 9.

Links

Crossrefs

Intersection of A000290 and A069570.
Cf. A069556, A069557, A069558, A069559.

Programs

  • PARI
    isok(k)={my(d=digits(k)); for(i=1, #d, my(t=d[#d+1-i]); if(!t || (t%i && i%t), return(0))); 1}
for(k=1, 10000, my(x=k^2); if(isok(x), print1(x, ", "))) \\ Andrew Howroyd, Sep 19 2024
  • PARI
    \\ faster program
B(k)={
  local(L=List());
  my(v=vector(k, i, select(t->t%i==0||i%t==0, [1..9])));
  my(chk(d)=for(i=1, #d, if(!vecsearch(v[i], d[#d+1-i]), return(0)));1);
  my(s=k\2, b=10^s);
  my(recurse(i,m)=if(i==s,
     for(j=sqrtint(m*b+b\10-1)+1, sqrtint(m*b+b-1), my(t=j^2); if(chk(digits(t%b)), listput(L,t))),
    m*=10; foreach(v[i], t, self()(i-1, m+t))
  ));
  recurse(k, 0);
  Vec(L);
}
concat(vector(12,k,B(k))) \\ Andrew Howroyd, Sep 19 2024

Extensions

More terms from Sascha Kurz, Mar 23 2002
Offset changed by Andrew Howroyd, Sep 19 2024

A225659 Primes p where p + sumOfDigits(p) +- 3 is prime.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 131, 137, 139, 157, 173, 179, 191, 197, 223, 227, 229, 241, 263, 269, 283, 311, 313, 317, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 463, 467, 487, 557
Offset: 1

Views

Author

John-Å. W. Olsen, May 11 2013

Keywords

Comments

a(n) = A068690(n), A030144(n), A069556(n), A091727(n), A156756(n) if n<14.

Examples

			If p = 409, then 409 + sod(409) +- 3 = 409+13 - 3 = 419, which is prime.
If p =  23, then  23 + sod(23)  +- 3 = 23+5   + 3 = 31,  which is prime.

Links

Crossrefs

Cf. A000040, A007605, A068690, A030144, A069556, A091727, A156756.

Programs

  • Mathematica
    Select[Prime[Range[102]],Or@@PrimeQ[#+Total[IntegerDigits[#]]+{3,-3}] &] (* Jayanta Basu, May 23 2013 *)
  • PARI
    ok(p)= {my(s=vecsum(digits(p)));isprime(p) && (isprime(p+s-3) || isprime(p+s+3))}
select(ok,[1..1000]) \\ Andrew Howroyd, Feb 22 2018
Showing 1-5 of 5 results.

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

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