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 1-4 of 4 results.

A094153 a(n) is least prime p such that 7 is the n-th term in the Euclid-Mullin sequence starting at p, or 0 if no such prime p exists.

Original entry on oeis.org

7, 0, 2, 43, 11, 13, 31, 149, 347, 23, 439, 223, 461, 173, 5, 71, 197, 1153, 191, 307, 1657, 971, 9473, 19, 2399, 1607, 6781, 89, 9187, 281, 23623, 15077, 25579, 17203
Offset: 1

Views

Author

Labos Elemer, May 05 2004

Keywords

Comments

The sequence is not monotonic. Compare to A093882.
Next term exceeds 50000. - Sean A. Irvine, Jan 12 2012

Examples

			a(5)=11 because p=7 first arises in EM at position 5, which is initiated with 11: {11,2,23,3,7,10627,433}; see A051309.

Crossrefs

Cf. A000945, A051308-A051334, A056756, A093777-A093783.

Extensions

Definition clarified, terms corrected and extended by Sean A. Irvine, Apr 15 2011
More terms from Sean A. Irvine, May 22 2011
25579 and 17203 from Sean A. Irvine, Jan 11 2012

A138953 Sum of numbers from all substrings of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15
Offset: 0

Views

Author

Zak Seidov, Apr 04 2008

Keywords

Examples

			One-digit numbers have no substring, hence a(0..9)=0;
a(10)  = 1+0 = 1,
a(123) = 1+2+3+12+23 = 41,
a(150) = 1+5+0+15+50 = 71.

Links

Crossrefs

Cf. A093882.

Programs

  • Mathematica
    Table[id=IntegerDigits[n]; Total[Flatten[Table[FromDigits/@ Partition[id,k,1], {k,Length[id]-1}]]], {n,0,150}]

Formula

a(n) = A071980(n) - n. [R. J. Mathar, Jul 06 2009]
Note: Mathar's formula works for numbers with 1, 2 or 3 digits, but thereafter only for numbers whose internal digits are zeros. [Christian N. K. Anderson, May 13 2013]

A307629 Let decimal expansion of n be d_1 d_2 ... d_k; a(n) = Sum_{i=1..k-1} Sum_{j=i+1..k} (d_i + d_j).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 2, 4, 6
Offset: 0

Views

Author

N. J. A. Sloane, Apr 19 2019

Keywords

Comments

More than the usual number of terms are shown in order to distinguish this from related sequences.
Starts to differ from A093882 at A093882(101)=22 <> a(101)=4. - R. J. Mathar, May 06 2019

Examples

			For n<10 there is only one decimal digit so a(n)=0.
a(102) = 1+0 + 1+2 + 0+2 = 6.

Links

Crossrefs

Cf. A007953, A055642, A110805, A138953.
Suggested by A307560.

Programs

  • Maple
    a:= n-> (d-> (nops(d)-1)*add(i, i=d))(convert(n, base, 10)):
seq(a(n), n=0..120);  # Alois P. Heinz, Apr 19 2019
  • Mathematica
    Array[Total@ Flatten@ Subsets[IntegerDigits@ #, {2}] &, 103, 0] (* Michael De Vlieger, Apr 19 2019 *)

Formula

From Alois P. Heinz, Apr 19 2019: (Start)
a(n) = A007953(n) * (A055642(n)-1).
a(n) = A110805(n) - A007953(n). (End)

A131639 Numbers n such that the sum of all numbers formed by deleting one digit from n is equal to n.

Original entry on oeis.org

1729404, 1800000, 13758846, 13800000, 14358846, 14400000, 15000000, 28758846, 28800000, 29358846, 29400000, 1107488889, 1107489042, 1111088889, 1111089042, 3277800000, 3281400000, 4388888889, 4388889042, 4392488889, 4392489042, 4500000000, 5607488889, 5607489042, 5611088889, 5611089042, 7777800000, 7781400000, 8888888889, 8888889042, 8892488889, 8892489042, 10000000000, 20000000000, 30000000000, 40000000000, 50000000000, 60000000000, 70000000000, 80000000000, 90000000000
Offset: 1

Views

Author

Jon Ayres (jonathan.ayres(AT)ntlworld.com), Sep 05 2007

Keywords

Comments

The sequence is complete. In general, a number x = x_1 x_2 ... x_n of n digits belongs to the sequence if its digits satisfy a certain Diophantine equation c_1*x_1 + c_2*x_2 + ... + c_n*x_n = 0, where the coefficients c_i depend on n. It is easy to verify that for n > 11 all the coefficient c_i are positive, so the equation does not admit a nonzero solution. - Giovanni Resta, Jul 20 2015

Examples

			First term is 1729404 because sum(1729404) = 729404 + 129404 + 179404 + 172404 + 172904 + 172944 + 172940 = 1729404.

Crossrefs

Cf. A093882.

Programs

  • PARI
    isok(n)=d = digits(n); if (sumdigits(n)*(#d-2) % 9 , return (0)); s = 0; for (i=1, #d, nd = vector(#d-1, j, if (i > j, d[j], d[j+1])); s += subst(Pol(nd), x, 10);); s == n; \\ Michel Marcus, Apr 24 2014

Formula

For a number with n digits there are n substrings generated by removing one digit from the original number. So for 12345, these are 2345, 1345, 1245, 1235, 1234. Sum(x) is defined as the sum of these substrings for a number x and the sequence above is those numbers such that sum(x) = x.

Extensions

a(12)-a(22) from Donovan Johnson, Jan 16 2011
a(23)-a(41) from Anthony Sand, Apr 24 2014
Showing 1-4 of 4 results.

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