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 1-10 of 26 results. Next

A376769 a(n) = digitsum of A302656(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 1, 8, 10, 17, 1, 9, 8, 9, 100, 2, 7, 2, 6, 3, 6, 19, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 16, 20, 15, 12, 2, 4, 19, 9, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 90, 10, 8, 11, 7, 12, 6, 13, 5, 2, 9, 7, 9, 2, 9, 9, 6, 9, 3, 9, 10, 11, 3, 2, 8, 9, 14, 4, 22, 14, 23, 3, 13, 3, 21, 25, 1, 10, 3, 5, 1000, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 8, 4
Offset: 1

Views

Author

N. J. A. Sloane, Nov 04 2024

Keywords

Comments

Of course, by the definition of A302656, the present sequence and A302656 have exactly the same sequence of digits (which is now A376771).

Links

Crossrefs

Cf. A007953, A302656, A376770, A376771.
Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A376776 Position of prime(n) in A302656, or -1 if prime(n) does not appear in A302656.

Original entry on oeis.org

2, 3, 5, 7, 21, 44, 13, 14, 49, 38, 50, 77, 96, 68, 78, 81, 83, 138, 401, 113, 149, 39, 181, 15, 1646, 43, 110, 161, 10, 153, 364, 162, 432, 1679, 471, 451, 1683, 425, 1691, 1615, 13649
Offset: 1

Views

Author

N. J. A. Sloane, Nov 06 2024

Keywords

Comments

The primes in A302656 do not appear in their natural order.

Examples

			Prime(5) = 11, and A302656(21) = 11, so a(5) = 11.
Prime(40) = 173, and A302656(1615) = 173, so a(40) = 1615.

Crossrefs

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

Extensions

a(41) = 13649 from Dominic McCarty's b-file for A376772 added by N. J. A. Sloane, Nov 21 2024

A377903 Indices of records in A302656.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 97, 176, 396, 463, 1918, 1984, 2278
Offset: 1

Views

Author

N. J. A. Sloane, Nov 19 2024

Keywords

Comments

Conjecture: a(n) = A377904(n-9) for n >= 11.
Based on Dominic McCarty's data in A302656.

Examples

			Table showing n, a(n) = index of n-th record in A302656, and the corresponding record value:
   1 1 1
   2 2 2
   3 3 3
   4 4 4
   5 5 5
   6 6 6
   7 7 7
   8 8 8
   9 9 9
   10 10 109
   11 20 199999999999
   12 97 2*10^111-1
   13 176 2*10^1111-1
   14 396 2*10^11111-1
   15 463 2*10^111111-1
   16 1918 2*10^1111111-1
   17 1984 2*10^11111111-1
   18 2278 2*10^111111111-1

Crossrefs

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A377904 Index of 2*10^((10^n-1)/9) - 1 in A302656, or -1 if that number never appears there.

Original entry on oeis.org

1, 14, 20, 97, 176, 396, 463, 1918, 1984, 2278
Offset: 0

Views

Author

N. J. A. Sloane, Nov 19 2024

Keywords

Comments

a(n) is the index in A302656 where we see 199...9, with k 9's, where k = 11...1 (with n 1's). For example, a(3) = 97 is where we see 199..9 with 111 9's.
It is extremely unlikely that -1 appears as a term in this sequence.
Based on Dominic McCarty's data in A302656.

Crossrefs

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A377906 Index of 10^n in A302656, or -1 if 10^n does not appear in A302656.

Original entry on oeis.org

1, 12, 16, 56, 93, 136, 168, 321, 332, 363, 409, 411, 443, 467, 1658, 1688, 1699, 1708, 1715, 1720, 1913
Offset: 0

Views

Author

N. J. A. Sloane, Nov 22 2024

Keywords

Comments

Also the indices of the 1's in A376769.
A term 10^n in A302656 is the trigger for an astronomically-sized term 2*10^{n 1's} - 1 later. For example, a(4) = 93 leads to the term A302656(176) = 2*10^1111 - 1 (cf. A377903, A377904).
a(0) through a(19) based on Dominic McCarty's data in A302656.
The initial 21 terms form three groups of sizes 7, 7, and at least 7. It would be nice to know more terms.

Crossrefs

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A376771 List of successive digits (the "digit stream") of A302656 (or, equally, A376769).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 9, 1, 8, 1, 0, 1, 7, 1, 9, 8, 9, 1, 0, 0, 2, 7, 2, 6, 3, 6, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 6, 2, 0, 1, 5, 1, 2, 2, 4, 1, 9, 9, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 1, 0, 8, 1, 1, 7, 1, 2, 6, 1, 3, 5, 2, 9, 7, 9, 2, 9, 9, 6, 9, 3, 9, 1, 0, 1, 1, 3, 2, 8, 9, 1, 4, 4, 2, 2, 1, 4, 2, 3, 3, 1, 3, 3, 2, 1, 2, 5, 1, 1, 0, 3, 5, 1
Offset: 1

Views

Author

N. J. A. Sloane, Nov 04 2024

Keywords

Links

Crossrefs

Cf. A302656, A376769.
Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A376772 Index where n appears in A302656, or -1 if n does not appear there.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 21, 25, 44, 48, 24, 22, 13, 11, 14, 23, 52, 47, 49, 26, 53, 18, 17, 58, 38, 75, 50, 65, 51, 61, 55, 19, 77, 60, 42, 84, 96, 63, 68, 59, 28, 94, 78, 62, 64, 135, 73, 132, 81, 29, 146, 131, 300, 89, 83, 141, 138, 109, 30, 148, 133, 317, 401, 86, 41, 143, 113, 31, 149, 165, 323, 452, 180, 124, 39, 117, 32, 315, 181, 369, 478, 447, 166, 128, 15, 33
Offset: 1

Views

Author

N. J. A. Sloane, Nov 04 2024; updated Nov 21 2024

Keywords

Comments

387 doesn't appear for n < 1262743. - Dominic McCarty, Nov 07 2024

Links

Crossrefs

Cf. A302656, A376776.
Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A377908 Difference between index of 10^n in A302656 and in A376769.

Original entry on oeis.org

0, 2, 4, 41, 83, 260, 295, 1597, 1652, 1915
Offset: 0

Views

Author

N. J. A. Sloane, Nov 22 2024

Keywords

Comments

Motivated by an attempt to explain the huge terms in A302656.
a(n) = A377904(n) - A377906(n).

Examples

			For n = 4, 10000 appears as A302656(93) and as A377904(176), so a(4) = 176-93 = 83. As a result, we get A302656(176) = 2*10^1111 - 1 = 199...9 (with 1111 9's).

Crossrefs

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A377911 Indices of the 1's in the digit stream A376771.

Original entry on oeis.org

1, 10, 13, 15, 17, 19, 23, 32, 44, 45, 46, 50, 52, 56, 68, 71, 74, 75, 77, 80, 94, 96, 97, 102, 107, 112, 116, 119, 120, 124, 157, 162, 165, 168, 169, 171, 172, 176, 183, 189, 192, 194, 213, 214, 215, 218, 227, 236, 238, 239
Offset: 1

Views

Author

N. J. A. Sloane, Nov 23 2024

Keywords

Comments

Given that A302656 contains exponentially long runs of 9's, there will be very long gaps in the present sequence.

Crossrefs

Summary: the 16 sequences derived from A302656 are A376769-A376776, A377903-A377904, A377906-A377911.

A383318 Lexicographically earliest sequence of distinct terms such that replacing each term k with prime(k) does not change the succession of digits.

Original entry on oeis.org

6455, 3, 5, 1, 12, 37, 15, 7, 4, 71, 77, 35, 33, 8, 9, 14, 91, 371, 92, 34, 346, 72, 53, 94, 79, 13, 923, 39, 359, 2, 41, 49, 140, 141, 721, 916, 724, 17, 31, 792, 27, 80, 98, 11, 54, 497, 159, 547, 95, 912, 760, 73, 10, 340, 952, 131, 25, 135, 47, 93, 739, 43
Offset: 1

Views

Author

Dominic McCarty, Apr 23 2025

Keywords

Examples

			Let b(n) = prime(a(n))
(a(n)): 6455, 3, 5, 1, 12, 37, 15, 7, 4, 71, 77, ...
(b(n)): 64553,   5, 11, 2, 37, 157,   47, 17, 7, ...

Links

Crossrefs

Cf. A383319 (prime(a(n))), A067928, A383320, A383322, A302656.

Programs

  • Python
    from sympy import prime
from itertools import count
a, sa, sb = [6455], "6455", "64553"
for _ in range(30):
    a.append(next(n for k in count(1) if not (n := int(sb[len(sa):len(sa)+k])) in a and not (len(sb) > len(sa) + k and sb[len(sa) + k] == "0")))
    sa += str(a[-1]); sb += str(prime(a[-1]))
print(a)
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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