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 10 results.

A066548 Sum of digits of n-th term of A066547.

Original entry on oeis.org

1, 5, 15, 25, 5, 15, 25, 20, 33, 33, 43, 46, 64, 63, 73, 90, 101, 117, 127, 27, 41, 55, 59, 61, 72, 89, 99, 109, 126, 137, 131, 70, 85, 100, 121, 141, 152, 170, 197, 135, 108, 145, 164, 189, 219, 240, 160, 167, 184, 227, 259, 282, 203, 207, 248, 275, 317, 297, 228
Offset: 1

Views

Author

Amarnath Murthy, Dec 16 2001

Keywords

Crossrefs

Cf. A066547.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003

A066581 Product of nonzero digits of A066547(n).

Original entry on oeis.org

1, 6, 120, 504, 2, 60, 336, 288, 40320, 15552, 1837080, 1327104, 309657600, 393750000, 2015539200, 94097687040, 1366159011840, 54793045278720, 140587147048320, 720, 3024, 120960, 10321920, 28343520, 334430208
Offset: 1

Views

Author

Amarnath Murthy, Dec 21 2001

Keywords

Examples

			The third term of A066547 is 456 hence a(3) = 120.

Crossrefs

Cf. A066547.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003

A007923 Lengths increase by 1, digits cycle through positive digits.

Original entry on oeis.org

1, 23, 456, 7891, 23456, 789123, 4567891, 23456789, 123456789, 1234567891, 23456789123, 456789123456, 7891234567891, 23456789123456, 789123456789123, 4567891234567891, 23456789123456789, 123456789123456789
Offset: 1

Views

Author

R. Muller

Keywords

References

  • C. Ashbacher, Some Problems Concerning the Smarandache Deconstructive Sequence, J. Recreational Mathematics, Vol. 29, No. 2, pages 82-84.
  • K. Atanassov, On the 4th Smarandache Problem, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 1, 33-35.

Links

Crossrefs

Cf. A001369, A007924, A050234, A066547.

Programs

  • Mathematica
    A007923[n_Integer] := Module[{result = 0},Do[ result += (Mod[(n*(n - 1)/2 + i - 1), 9] + 1) * 10^(n - i),{i, 1, n}   ]; result ]; Table[A007923[n],{n,18}] (* James C. McMahon, Dec 04 2023 *)
  • PARI
    a(n)=my(m=(n*(n+1)/2-1)%9); sum(k=0,n-1,10^k*((m-k)%9+1))

Formula

a(n) = (10^9+1) a(n-9) - 10^9 a(n-18), n>=18. - corrected by Michael Somos, Sep 28 2002
a(n) = Sum_{i=1..n} ((n*(n-1)/2+i-1 mod 9)+1)*10^(n-i). - Vedran Glisic, Apr 08 2011
a(n) = floor(10^(n*(n+1)/2)*123456789/999999999) - 10^n*floor(10^(n*(n-1)/2)*123456789/999999999). - Néstor Jofré, Jun 03 2017

A066549 Let N = 235711171923293137..., the concatenation of the primes. a(n) is the n-digit number formed from the digits of N starting from the {n(n-1)/2 +1}th digit. Omit any leading zeros.

Original entry on oeis.org

2, 35, 711, 1317, 19232, 931374, 1434753, 59616771, 737983899, 7101103107, 10911312713, 113713914915, 1157163167173, 17918119119319, 719921122322722, 9233239241251257, 26326927127728128, 329330731131331733
Offset: 1

Views

Author

Amarnath Murthy, Dec 16 2001

Keywords

Links

Crossrefs

Cf. A033308, A066547.

Programs

  • Mathematica
    Module[{nn=500,cp},cp=Flatten[IntegerDigits/@Prime[Range[nn]]];Table[ FromDigits[ Take[cp,{(2-n+n^2)/2,(n(n+1))/2}]],{n,(Sqrt[1+8nn]-1)/2}]] (* Harvey P. Dale, Jul 07 2016 *)

Extensions

More terms from Sascha Kurz, Jan 28 2003

A001369 Blocks of increasing length using 1,2,3,...,9,10; omit leading 0's.

Original entry on oeis.org

1, 23, 456, 7891, 1234, 567891, 123456, 78910123, 456789101, 2345678910, 12345678910, 123456789101, 2345678910123, 45678910123456, 789101234567891, 123456789101234, 56789101234567891, 12345678910123456, 7891012345678910123, 45678910123456789101
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

It appears that the first digit repeats 1, 2, 4, 7, 1, 5, 1, 7, 4, 2, 1. - T. D. Noe, Apr 05 2011

Links

Crossrefs

Cf. A066547, A007923.

Programs

  • Mathematica
    nn = 20; d = Flatten[Table[{1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0}, {Ceiling[nn (nn + 1)/22]}]]; Table[e = (n + 1) n/2; s = e - n + 1; FromDigits[d[[s ;; e]]], {n, nn}] (* T. D. Noe, Apr 05 2011 *)
  • PARI
    N=[]; k=Mod(-1,10); for(n=1, 20, while(#NM. F. Hasler, May 08 2014

A066551 Let N =149162536496481100121441691962252562893243614..., the concatenation of the squares. a(n) is the n-digit number formed from the digits of N starting from the {n(n-1)/2 +1}th digit. Omit any leading zeros.

Original entry on oeis.org

1, 49, 162, 5364, 96481, 100121, 1441691, 96225256, 289324361, 4004414845, 29576625676, 729784841900, 9611024108911, 56122512961369, 144415211600168, 1176418491936202, 52116220923042401, 250026012704280929, 1630253136324933643, 48136003721384439694, 96422543564489462447
Offset: 1

Views

Author

Amarnath Murthy, Dec 16 2001

Keywords

Comments

Are there any squares in this sequence other than 1 and 49?
No other squares in a(3)..a(10^5). - Michael S. Branicky, May 23 2025

Links

Crossrefs

Cf. A066547, A066549.

Programs

  • Mathematica
    With[{c=Flatten[IntegerDigits/@(Range[100]^2)]},Table[FromDigits[Take[c,{(n(n-1))/2+1,(n(n-1))/2+n}]],{n,20}]] (* Harvey P. Dale, Jul 21 2012 *)
  • Python
    from itertools import count, islice
def agen(): # generator of terms
    N, i = [], 1
    for n in count(1):
        target = n*(n-1)//2
        while len(N) <= target+n+1:
            N.extend(list(str(i**2)))
            i += 1
        yield int("".join(N[target:target+n]))
print(list(islice(agen(), 21))) # Michael S. Branicky, May 23 2025

Extensions

Corrected and extended by Lior Manor, Feb 13 2002
a(19) and beyond from Michael S. Branicky, May 23 2025

A100751 Concatenate all natural numbers starting with 1 in binary like this 11011100101110111100010011010..., then a(n) = the number formed from the next n digits (by dropping leading zeros). 1, 10, 111, 0010, 11101, 111000, ... 1, 10, 111, 10, 11101, 111000, ...

Original entry on oeis.org

1, 10, 111, 10, 11101, 111000, 1001101, 1011110, 11011110, 1111100001, 11001010, 11101001010, 1101101011111, 11001110101, 101111100111011, 1110111111000001, 1100010100011, 100100100101100110, 1001111010001010011
Offset: 1

Views

Author

Amarnath Murthy, Nov 20 2004

Keywords

Examples

			1, 10, 111, 0010, 11101, 111000, ... becomes
1, 10, 111, 10, 11101, 111000, ...

Links

Crossrefs

Cf. A066547, A100489.

Programs

  • Mathematica
    d = Flatten[ Table[ IntegerDigits[n, 2], {n, 45}]]; Table[ FromDigits[ Take[d, {n(n + 1)/2 + 1, (n + 1)(n + 2)/2}]], {n, 0, 18}] (* Robert G. Wilson v, Nov 22 2004 *)
Module[{nn=50,b,x},b=Flatten[IntegerDigits[Range[nn],2]];x = Floor[ (Sqrt[1+8 Length[ b]]-1)/2];FromDigits[#]&/@TakeList[b,Range[x]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jan 21 2021 *)

Extensions

More terms from Robert G. Wilson v, Nov 22 2004

A100489 Decimal equivalents of numbers in A100751.

Original entry on oeis.org

1, 2, 7, 2, 29, 56, 77, 94, 222, 993, 202, 1866, 7007, 1653, 24379, 61377, 6307, 149862, 324691, 350053, 1502192, 3263293, 1764799, 1897951, 20839416, 4293902, 19056271, 35965591, 105749822, 558273850, 1253419992, 3010125259, 6163513735
Offset: 1

Views

Author

Amarnath Murthy and Robert G. Wilson v, Nov 22 2004

Keywords

Links

Crossrefs

Cf. A100751, A066547.

Programs

  • Mathematica
    d = Flatten[Table[IntegerDigits[n, 2], {n, 100}]]; Table[FromDigits[Take[d, {n(n + 1)/2 + 1, (n + 1)(n + 2)/2}], 2], {n, 0, 32}]

A066550 Sum of digits of n-th term of A066549.

Original entry on oeis.org

2, 8, 9, 12, 17, 27, 27, 42, 63, 21, 29, 45, 49, 61, 52, 60, 75, 56, 88, 94, 83, 119, 98, 139, 105, 131, 147, 158, 185, 182, 107, 91, 88, 90, 113, 118, 129, 135, 155, 166, 173, 188, 189, 204, 191, 147, 124, 183, 176, 197, 208, 253, 251, 254, 240, 194, 199, 218, 243
Offset: 1

Views

Author

Amarnath Murthy, Dec 16 2001

Keywords

Crossrefs

Cf. A033308, A066547, A066549.

Extensions

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003

A066552 Sum of digits of n-th term of A066551.

Original entry on oeis.org

1, 13, 9, 18, 28, 5, 26, 37, 38, 34, 61, 59, 43, 58, 44, 64, 44, 59, 67, 85, 98, 89, 109, 121, 124, 144, 47, 82, 94, 104, 135, 139, 145, 103, 95, 135, 184, 162, 143, 173, 157, 151, 198, 194, 199, 218, 148, 234, 231, 261, 257, 226, 297, 169, 192, 179, 163, 195, 216
Offset: 1

Views

Author

Amarnath Murthy, Dec 16 2001

Keywords

Crossrefs

Cf. A066547, A066549, A066551.

Programs

  • Mathematica
    With[{c=Flatten[IntegerDigits/@(Range[400]^2)]},Table[Total[Take[c,{(n(n-1))/2+1,(n(n-1))/2+n}]],{n,60}]] (* Harvey P. Dale, Jul 21 2012 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 01 2003
Showing 1-10 of 10 results.

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

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