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.

A169640 Numbers k such that sum of digits of the k-th prime = the sum of digits of the k-th semiprime.

Original entry on oeis.org

23, 31, 38, 52, 54, 62, 84, 93, 98, 111, 118, 135, 150, 201, 209, 215, 228, 258, 266, 288, 299, 330, 348, 352, 379, 399, 400, 471, 476, 479, 488, 500, 509, 511, 533, 538, 540, 545, 560, 585, 598, 618, 624, 629, 678, 693, 714, 720, 751, 752, 759, 771, 790, 805
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 04 2010

Keywords

Examples

			a(1)=23 because 23rd prime=83(8+3=11) and 23rd semiprime=65(6+5=11).

Links

Crossrefs

Cf. A007605, A175013.

Programs

Formula

A007605(a(n)) = A175013(a(n)).
A007953(A000040(n)) = A007953(A001358(n)). - Ray Chandler, Apr 05 2010

Extensions

Edited by N. J. A. Sloane, Apr 05 2010
Edited, corrected and extended by Ray Chandler, Apr 05 2010

A176543 Numbers k such that semiprime(k)/sum of digits of semiprime(k) is prime.

Original entry on oeis.org

7, 36, 44, 63, 68, 79, 128, 148, 157, 192, 244, 303, 323, 335, 410, 421, 475, 483, 535, 606, 616, 669, 776, 849, 862, 868, 947, 964, 986, 1039, 1046, 1256, 1264, 1403, 1406, 1422, 1579, 1700, 1733, 1874, 1971
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 20 2010

Keywords

Examples

			7 is a term because 7 (prime) = 21/3 = semiprime(7)/sum of digits of semiprime(7);
36 is a term because 37 (prime) = 111/3 = semiprime(36)/sum of digits of semiprime(36).

Crossrefs

Cf. A001358 (semiprimes), A007953 (sum of digits), A175013.

Programs

  • Maple
    A175013 := proc(n) A007953(A001358(n)) ; end proc: A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc: for n from 1 to 2000 do r := A001358(n)/A175013(n) ; if type(r,'integer') then if isprime(r) then printf("%d,",n) ; end if; end if; end do: # R. J. Mathar, Apr 26 2010

Formula

A001358(a(n))/A175013(a(n)) is prime.

Extensions

More terms from R. J. Mathar, Apr 26 2010

A176544 Primes of the form semiprime(k)/sum of digits of semiprime(k).

Original entry on oeis.org

7, 37, 19, 67, 19, 19, 37, 37, 73, 37, 73, 337, 367, 163, 73, 109, 127, 73, 109, 163, 127, 181, 163, 433, 181, 163, 199, 181, 271, 163, 199, 199, 271, 271, 397, 307, 307, 487, 379, 541, 433, 577, 397, 271, 631, 433, 379, 487, 919, 1459, 541, 937, 811, 631, 991
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 20 2010

Keywords

Examples

			7 is a term because 7 = 21/(2+1);
37 is a term because 37 = 111/(1+1+1).

Links

Crossrefs

Cf. A001358 (semiprimes), A007953 (sum of digits), A175013, A176543.

Programs

  • Maple
    A175013 := proc(n) A007953(A001358(n)) ; end proc: A007953 := proc(n) add(d,d=convert(n,base,10)) ; end proc: for n from 1 to 4000 do r := A001358(n)/A175013(n) ; if type(r,'integer') then if isprime(r) then printf("%d,",r) ; end if; end if; end do: # R. J. Mathar, Apr 26 2010
  • Mathematica
    Select[#/Total[IntegerDigits[#]]&/@Select[Range[30000],PrimeOmega[#]==2&],PrimeQ] (* Harvey P. Dale, Aug 10 2023 *)

Formula

a(n) = p = A001358(n)/A175013(n).
a(n) = A001358(A176543(n))/A175013(A176543(n)). - R. J. Mathar, Apr 26 2010

Extensions

More terms from R. J. Mathar, Apr 26 2010

A257652 The semiprimes which set new records for the sum of their decimal digits.

Original entry on oeis.org

4, 6, 9, 38, 39, 49, 69, 169, 278, 289, 299, 489, 589, 689, 699, 799, 899, 2899, 3899, 4989, 5899, 5999, 6999, 7999, 9899, 19999, 29999, 48999, 58999, 68999, 69999, 88999, 99899, 299899, 398999, 589989, 589999, 689999, 798999, 889999, 899999, 2899999, 3899999
Offset: 1

Views

Author

K. D. Bajpai, Jul 25 2015

Keywords

Comments

The semiprimes that set new records in A175013. New records of digit sums of 4, 6, 9, 11, 12, 13, 15, 16, 17,.. are set by the semiprimes 4, 6, 9, 38, 39, 49, 69,...

Examples

			a(4) = 38 = 2 * 19, which is a semiprime with sum of digits = 3 + 8 = 11.
a(5) = 39 = 3 * 13, which is a semiprime with sum of digits = 3 + 9 = 12. Since 12 > 11, 38 and 39 are in list.

Links

Crossrefs

Cf. A175013, A068809, A246569.
Subsequence of A213653.

Programs

  • Mathematica
    t = {}; s = 0; Do[If[(x = Total[IntegerDigits[n]]) > s && PrimeOmega[n] == 2, AppendTo[t, n]; s = x], {n, 1000000}];t
DeleteDuplicates[{#,Total[IntegerDigits[#]]}&/@Select[Range[4*10^6],PrimeOmega[#] == 2&],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Apr 12 2024 *)
Showing 1-4 of 4 results.

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

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