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 1-7 of 7 results.

A032763 Take list of even numbers, move left digit of each term to end of previous term.

Original entry on oeis.org

0, 2, 4, 6, 8, 1, 1, 21, 41, 61, 82, 2, 22, 42, 62, 83, 3, 23, 43, 63, 84, 4, 24, 44, 64, 85, 5, 25, 45, 65, 86, 6, 26, 46, 66, 87, 7, 27, 47, 67, 88, 8, 28, 48, 68, 89, 9, 29, 49, 69, 81, 1, 21, 41, 61, 81, 101, 121, 141, 161, 181, 201, 221, 241, 261, 281, 301, 321, 341
Offset: 0

Views

Author

Patrick De Geest, May 15 1998

Keywords

Examples

			Here is how the first few terms are obtained: from 0 2 4 6 8 10 12 14 16 ... we get 0/ 2/ 4/ 6/ 8/ 1/0 1/2 1/4 1/6 ... hence 0,2,4,6,8,1,1,21,41,61,...

Links

Crossrefs

Cf. A032759-A032764.
Cf. A005843.

Programs

  • Haskell
    a032763 n = a032763_list !! n
a032763_list = 0 : map read (zipWith (++) vs (tail us)) :: [Integer]
   where (us,vs) = unzip $ map ((splitAt 1) . show) [0, 2 ..]
-- Reinhard Zumkeller, Oct 10 2013

A032764 Take list of odd numbers, move left digit of each term to end of previous term.

Original entry on oeis.org

1, 3, 5, 7, 9, 1, 11, 31, 51, 71, 92, 12, 32, 52, 72, 93, 13, 33, 53, 73, 94, 14, 34, 54, 74, 95, 15, 35, 55, 75, 96, 16, 36, 56, 76, 97, 17, 37, 57, 77, 98, 18, 38, 58, 78, 99, 19, 39, 59, 79, 91, 11, 31, 51, 71, 91, 111, 131, 151, 171, 191, 211, 231, 251, 271, 291, 311
Offset: 0

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032759-A032762.
Cf. A005408.

Programs

  • Haskell
    a032764 n = a032764_list !! n
a032764_list = 1 : map read (zipWith (++) vs (tail us)) :: [Integer]
   where (us,vs) = unzip $ map ((splitAt 1) . show) [1, 3 ..]
-- Reinhard Zumkeller, Oct 10 2013

A032762 Take list of integers n >= 0, move left digit of each term to end of previous term.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 11, 21, 31, 41, 51, 61, 71, 81, 92, 2, 12, 22, 32, 42, 52, 62, 72, 82, 93, 3, 13, 23, 33, 43, 53, 63, 73, 83, 94, 4, 14, 24, 34, 44, 54, 64, 74, 84, 95, 5, 15, 25, 35, 45, 55, 65, 75, 85, 96, 6, 16, 26, 36, 46, 56, 66, 76, 86, 97, 7, 17, 27
Offset: 0

Views

Author

Patrick De Geest, May 15 1998

Keywords

Examples

			...,15,16,17,18,19,... -> ...,51,61,71,81,...

Links

Crossrefs

Cf. A032759-A032764.

Programs

  • Haskell
    a032762 n = a032762_list !! n
a032762_list = 0 : map read (zipWith (++) vs (tail us)) :: [Integer]
   where (us,vs) = unzip $ map ((splitAt 1) . show) [0..]
-- Reinhard Zumkeller, Oct 10 2013

A197124 Extract positive numbers from the infinite string of prime numbers 235711131719..., constructing the smallest numbers which have not appeared in an earlier extraction.

Original entry on oeis.org

2, 3, 5, 7, 1, 11, 31, 71, 9, 23, 29, 313, 74, 14, 34, 75, 35, 96, 16, 77, 17, 37, 98, 38, 99, 710, 110, 310, 7109, 113, 12, 713, 1137, 13, 91, 4, 915, 115, 716, 316, 717, 317, 918, 119, 1193, 19, 719, 92, 112, 232, 27, 22, 923, 32, 39, 24, 125, 1257, 26
Offset: 1

Views

Author

Yves Debeuret, Oct 10 2011

Keywords

Comments

The infinite stream of prime digits is basically chopped into slices such that each of the digits is used exactly once and the outcoming stream does not contain duplicates.

Examples

			The initial digits 2, 3, 5, 7 and 1 are all extracted in the order of occurrence. The next 1 is rejected because it appeared earlier, and united with the (overall) third 1 to extract 11. The next 3 (from 13) appeared already earlier and is combined with the following 1 (from the 17) to created 31.

Links

Crossrefs

Cf. A032759, A228595.

Programs

  • Mathematica
    nn=100; digs = Flatten[Table[IntegerDigits[Prime[n]], {n, nn}]]; numList = {}; While[digs != {}, num = 0; While[num = num*10 + digs[[1]]; digs = Rest[digs]; newNum = ! MemberQ[numList, num]; (num == 0 || ! newNum) && digs != {}]; If[newNum, AppendTo[numList, num]]]; numList (* T. D. Noe, Oct 31 2011 *)
  • Python
    from sympy import nextprime
from itertools import islice
def diggen():
    p = 2
    while True:
        yield from list(map(int, str(p)))
        p = nextprime(p)
def agen(): # generator of terms
    g = diggen()
    aset, nextd = set(), next(g)
    while True:
        an, nextd = nextd, next(g)
        while an in aset or nextd == 0:
            an, nextd = int(str(an) + str(nextd)), next(g)
        yield an
        aset.add(an)
print(list(islice(agen(), 80))) # Michael S. Branicky, Mar 31 2022

A032760 Take list of squares, move left digit of each term to end of previous term.

Original entry on oeis.org

0, 1, 4, 9, 1, 62, 53, 64, 96, 48, 11, 1, 211, 441, 691, 962, 252, 562, 893, 243, 614, 4, 414, 845, 295, 766, 256, 767, 297, 848, 419, 9, 611, 241, 891, 1561, 2251, 2961, 3691, 4441, 5211, 6001, 6811, 7641, 8491, 9362, 252, 1162, 2092, 3042, 4012, 5002, 6012
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032759-A032764.
Cf. A000290.

Programs

  • Haskell
    a032760 n = a032760_list !! n
a032760_list = 0 : map read (zipWith (++) vs (tail us)) :: [Integer]
   where (us,vs) = unzip $ map ((splitAt 1) . show) a000290_list
-- Reinhard Zumkeller, Oct 10 2013

A032761 Take list of cubes, move left digit of each term to end of previous term.

Original entry on oeis.org

0, 1, 8, 2, 76, 41, 252, 163, 435, 127, 291, 1, 3311, 7282, 1972, 7443, 3754, 964, 9135, 8326, 8598, 9, 2611, 6481, 21671, 38241, 56251, 75761, 96832, 19522, 43892, 70002, 97913, 27683, 59373, 93044, 28754, 66565, 6535, 48725, 93196, 40006, 89217, 40887
Offset: 0

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032759-A032764.
Cf. A000578.

Programs

  • Haskell
    a032761 n = a032761_list !! n
a032761_list = 0 : map read (zipWith (++) vs (tail us)) :: [Integer]
   where (us,vs) = unzip $ map ((splitAt 1) . show) a000578_list
-- Reinhard Zumkeller, Oct 10 2013

A381224 a(n) is the integer resulting from the concatenation of the unit digit of prime(n-1) to the digits of prime(n) without its own unit digit.

Original entry on oeis.org

0, 2, 3, 5, 71, 11, 31, 71, 92, 32, 93, 13, 74, 14, 34, 75, 35, 96, 16, 77, 17, 37, 98, 38, 99, 710, 110, 310, 710, 911, 312, 713, 113, 713, 914, 915, 115, 716, 316, 717, 317, 918, 119, 119, 319, 719, 921, 122, 322, 722, 923, 323, 924, 125, 125, 726, 326, 927, 127, 728, 128, 329, 330, 731, 131, 331, 733, 133, 734, 734, 935, 335
Offset: 1

Views

Author

N. J. A. Sloane, Feb 22 2025

Keywords

Comments

Take list of primes and move the right-most digit of each term to the start of the next term.
Inspired by Eric Angelini and Carole Dubois's A339467.

Examples

			Starting from
   2, 3, 5, 7, 11, 13, 17, 19, ...
we get
   0, 2, 3, 5, 71, 11, 31, 71, ...

Links

Crossrefs

Cf. A000040, A032759, A290148, A339467.

Programs

  • Maple
    a381224 := proc(n) local i,p;
if n=1 then i:=0; else i:=(ithprime(n-1) mod 10); fi;
p:=ithprime(n);
i * 10^ilog10(p) + floor(p/10);
end;
  • Python
    from sympy import prime
def a(n): return 0 if n == 1 else int(str(prime(n-1)%10)+ str(prime(n))[:-1])
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Feb 22 2025
Showing 1-7 of 7 results.

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

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