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 97 results. Next

A377472 First differences of Colombian or self numbers A003052.

Original entry on oeis.org

2, 2, 2, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 11, 2, 11, 11, 11, 11, 11, 11, 11, 11, 15, 11
Offset: 1

Views

Author

M. F. Hasler, Oct 29 2024

Keywords

Comments

Most terms are equal to 11.
Up to a(103) = 15, the only exceptions are a(n) = 2 for n = 1, 2, 3, 4, 14, 24, ..., 94.
Then a(n) = 2 for n = 112, 122, ..., 192, and a(201) = 15.
Then a(n) = 2 for n = 210, 220, ..., 290, and a(299) = 15.
This pattern repeats 8 times, with a(n) = 15 for n = 397, 495, ..., 887.
Then a(984) = 28, after which the previous pattern resumes, with a(n) = 2 for n = 992, 1002, ..., 1072, then a(n) = 15 for n = 1081, 1179, ..., 1865.
This larger pattern continues with a(n) = 28 for n = 1962, 2940, 3918, ..., 8808.
A still larger pattern starts at a(9785) = 41, after which the previous pattern repeats with a(9881) = 15, later a(10762) = 28 etc.

Links

Crossrefs

Cf. A003052 (Colombian or self numbers), A377473 (range of this sequence), A377474 (indices where new terms appear), A163128, A163139.

Programs

  • PARI
    A377472_upto(N=99)={my(o,L=List()); for(n=1+o=1,oo,if(is_A003052(n), listput(L,n-o); o=n; #L

Formula

a(n) = A003052(n+1) - A003052(n).
a(n) = A163139(n) + 1 = A163128(n+1) - A163128(n) + 1. - Max Alekseyev, Jan 02 2025

A249045 Self-numbers (A003052) that are multiples of 3.

Original entry on oeis.org

3, 9, 42, 75, 108, 132, 165, 198, 222, 255, 288, 312, 345, 378, 411, 435, 468, 501, 525, 558, 591, 615, 648, 681, 714, 738, 771, 804, 828, 861, 894, 918, 951, 984, 1032, 1065, 1098, 1122, 1155, 1188, 1212, 1245, 1278, 1311, 1335, 1368, 1401, 1425, 1458, 1491
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2014

Keywords

References

  • D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.

Links

Crossrefs

Cf. A003052, A249046-A249048.

Programs

  • Haskell
    a249045 n = a249045_list !! (n-1)
a249045_list = filter ((== 0) . flip mod 3) a003052_list
-- Reinhard Zumkeller, Oct 31 2014

A249048 Self-numbers (A003052) that are multiples of 9.

Original entry on oeis.org

9, 108, 198, 288, 378, 468, 558, 648, 738, 828, 918, 1098, 1188, 1278, 1368, 1458, 1548, 1638, 1728, 1818, 1917, 2007, 2088, 2178, 2268, 2358, 2448, 2538, 2628, 2718, 2817, 2907, 2997, 3078, 3168, 3258, 3348, 3438, 3528, 3618, 3717, 3807, 3897, 3987, 4068, 4158, 4248
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2014

Keywords

References

  • D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.

Links

Crossrefs

Cf. A003052, A249045-A249047.

Programs

  • Haskell
    a249048 n = a249048_list !! (n-1)
a249048_list = filter ((== 0) . flip mod 9) a003052_list
-- Reinhard Zumkeller, Oct 31 2014

A171673 Numbers n with property that both n and n^2 are self numbers (A003052).

Original entry on oeis.org

1, 3, 20, 86, 97, 110, 176, 187, 266, 277, 356, 367, 457, 637, 714, 716, 727, 804, 815, 894, 984, 1087, 1177, 1267, 1357, 1436, 1537, 1614, 1616, 1627, 1704, 1715, 1884, 1985, 2077, 2235, 2257, 2516, 2694, 2784, 2885, 3045, 3135, 3315, 3326, 3337, 3414
Offset: 1

Views

Author

Zak Seidov, Dec 15 2009

Keywords

Links

Crossrefs

Cf. A003052 (Self or Colombian numbers), A171671 (self squares), A171672 (n^2 are self squares).

Programs

  • Mathematica
    nn=1.2*10^7; list=Table[n + Total[IntegerDigits[n]],{n,nn}]; se=Complement[Range[nn],list]; se1=Select[Sqrt[se],IntegerQ[#]&]; Intersection[se,se1] (* Jayanta Basu, May 06 2013 *)

Extensions

Changed the word "safe" in this entry to "self". - N. J. A. Sloane, Feb 26 2017

A374101 Numbers k such that k and k+2 are both self numbers (A003052).

Original entry on oeis.org

1, 3, 5, 7, 108, 209, 310, 411, 512, 613, 714, 815, 916, 1109, 1210, 1311, 1412, 1513, 1614, 1715, 1816, 1917, 2110, 2211, 2312, 2413, 2514, 2615, 2716, 2817, 2918, 3111, 3212, 3313, 3414, 3515, 3616, 3717, 3818, 3919, 4112, 4213, 4314, 4415, 4516, 4617, 4718
Offset: 1

Views

Author

Amiram Eldar, Jun 28 2024

Keywords

Comments

The least difference between consecutive self numbers is 2 (see Griffin N. Macris's proof at A010061 that may be adapted to other bases).

Links

Crossrefs

Subsequence of A003052.
Cf. A010061, A339216 (binary analog).

Programs

  • Mathematica
    seq[max_] := Module[{c = Complement[Range[max], Table[n + DigitSum[n], {n, 1, max}]], d, ind}, d = Differences[c]; ind = Position[d, 2] // Flatten; c[[ind]]]; seq[5000]

A249046 Self-numbers (A003052) that are multiples of 3 but not of 9.

Original entry on oeis.org

3, 42, 75, 132, 165, 222, 255, 312, 345, 411, 435, 501, 525, 591, 615, 681, 714, 771, 804, 861, 894, 951, 984, 1032, 1065, 1122, 1155, 1212, 1245, 1311, 1335, 1401, 1425, 1491, 1515, 1581, 1614, 1671, 1704, 1761, 1794, 1851, 1884, 1941, 1974, 2022, 2055, 2112, 2145
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2014

Keywords

References

  • D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.

Links

Crossrefs

Cf. A003052, A249045-A249048.

Programs

  • Haskell
    a249046 n = a249046_list !! (n-1)
a249046_list = filter ((> 0) . flip mod 9) a249045_list
-- Reinhard Zumkeller, Oct 31 2014

A249047 Self-numbers (A003052) that are not divisible by 3.

Original entry on oeis.org

1, 5, 7, 20, 31, 53, 64, 86, 97, 110, 121, 143, 154, 176, 187, 209, 211, 233, 244, 266, 277, 299, 310, 323, 334, 356, 367, 389, 400, 413, 424, 446, 457, 479, 490, 512, 514, 536, 547, 569, 580, 602, 613, 626, 637, 659, 670, 692, 703, 716
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2014

Keywords

References

  • D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.

Links

Crossrefs

Cf. A003052, A249045-A249048.

Programs

  • Haskell
    a249047 n = a249047_list !! (n-1)
a249047_list = filter ((> 0) . flip mod 3) a003052_list
-- Reinhard Zumkeller, Oct 31 2014

A382166 Self-numbers (A003052) that are cubes.

Original entry on oeis.org

1, 64, 512, 1728, 35937, 50653, 195112, 287496, 300763, 314432, 681472, 804357, 884736, 1000000, 2248091, 2744000, 3241792, 4173281, 4913000, 5929741, 6434856, 6859000, 10077696, 10360232, 12167000, 13481272, 15813251, 18399744, 19902511, 22188041, 27270901, 29791000, 36264691, 37933056, 47045881
Offset: 1

Views

Author

N. J. A. Sloane, Mar 26 2025

Keywords

Links

Crossrefs

Intersection of A000578 and A003052.
Cf. A171671.

A163125 Sum of digits of the n-th Self-number (or Colombian number), A003052(n).

Original entry on oeis.org

1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 12, 14, 16, 9, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 4, 6, 8, 10, 12, 14, 16, 18, 20, 4, 6, 8, 10, 12, 14, 16, 18, 20, 4, 6, 8, 10, 12, 14, 16, 18, 20, 13, 6, 8, 10, 12, 14, 16, 18, 20, 13, 15, 8, 10, 12, 14, 16, 18, 20, 13, 15, 17, 10, 12, 14, 16, 18, 20, 13
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jul 21 2009

Keywords

Examples

			a(6) = 2 + 0 = 2;
a(7) = 3 + 1 = 4.

Links

Crossrefs

Cf. A003052, A007953.

Programs

  • Maple
    A007953 := proc(n) add( d,d= convert(n,base,10) ); end:
isA003052 := proc(n) local k ; for k from 0 to n do if k+A007953(k) = n then RETURN(false): fi; od: RETURN(true) ; end:
A003052 := proc(n) option remember; if n = 1 then 1; else for a from procname(n-1)+1 do if isA003052(a) then RETURN(a) ; fi; od; fi; end:
A163125 := proc(n) A007953( A003052(n)) ; end: seq(A163125(n),n=1..100) ; # R. J. Mathar, Jul 27 2009
  • Mathematica
    sumdig[n_] := Plus @@ IntegerDigits[n]; m = 500; sumdig /@ Complement[Range[m], Table[n + sumdig[n], {n, 1, m}]] (* Amiram Eldar, Nov 28 2020 *)

Formula

a(n) = A007953(A003052(n)).

Extensions

Values after a(51) corrected by R. J. Mathar, Jul 27 2009

A282711 a(n) is the number of terms of A003052 that are <= n.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12
Offset: 1

Views

Author

N. J. A. Sloane, Feb 27 2017

Keywords

Links

Crossrefs

Cf. A003052.

Programs

  • Maple
    # Assumes the array b52 contains a list of the terms in A003052.
p:=[]; t:=1; m:=b52[t]; c:=1;
for n from 1 to 1000 do
if n=m then c:=c+1; t:=t+1; m:=b52[t]; fi;
p:=[op(p),c];
od:
p;

Formula

Zannier shows that a(n) = L*n + O((log x)^2), where L is approximately 10.227...
Showing 1-10 of 97 results. Next

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

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