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 1-6 of 6 results.

A327914 The 58 prime dates of each non-leap year of the form concatenate(month,day) with leading zero for days 1..9.

Original entry on oeis.org

101, 103, 107, 109, 113, 127, 131, 211, 223, 227, 307, 311, 313, 317, 331, 401, 409, 419, 421, 503, 509, 521, 523, 601, 607, 613, 617, 619, 701, 709, 719, 727, 809, 811, 821, 823, 827, 829, 907, 911, 919, 929, 1009, 1013, 1019, 1021, 1031, 1103, 1109, 1117, 1123, 1129, 1201, 1213, 1217, 1223, 1229, 1231
Offset: 1

Views

Author

Wolfdieter Lang, Sep 30 2019

Keywords

Comments

All these dates come in non-leap years from the months January, February, ..., December, in the form m.d, with a 0 in front of the days 1..9, with 7, 3, 5, 4, 4, 5, 4, 6, 4, 5, 5, 6 prime dates, respectively, adding up to 58. For the corresponding leap year case with 59 prime dates see A327915.
Comparing with A327914 (no leap year, no 0 in front of days d = 1..9) one finds the number differences for the months 0, -2, -1, -2+1 = -1, 0, 0, -1, -1, -1+1 = 0, -3, +1, -1+1 = 0, respectively. For a month with difference 0 (Jan, May, Jun) one just has to add a zero before the days 1..9 in A327914. In the other cases a -x indicates that x dates are no longer prime after insertion of a 0 before days 1..9, and +1 indicates that a new prime date appears: Feb: 203 and 209 out, Mar: 301 out, Apr: 403 and 407 out, 409 in, Jul: 703 out, Aug: 803 out, Sep: 907 out, 901 in, Oct 101, 103 and 107 out, Nov: 1109 in, Dec: 1207 out, 1201 in.

Crossrefs

Cf. A327346 (74 prime dates d.m without leading 0 for month), A327347 (54 prime dates d.m with leading 0 for months m = 1, 3, 7, 9), A327348 (66 prime dates m.d for non-leap years), A327349 (67 prime dates, like A327348 but for leap years), A327915 (59 prime dates, for leap years).

Programs

  • Mathematica
    Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[m~Join~PadLeft[IntegerDigits[#], 2]] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 28, True, 31]} &, 12], PrimeQ] (* Michael De Vlieger, Oct 03 2019 *)
fd[{m_,d_}]:=FromDigits[Flatten[{m,PadLeft[{d},2,0]}]]; Select[fd[Take[#,{2,3}]]&/@ DateRange[ {2023,1,1},{2023,12,31}],PrimeQ] (* Harvey P. Dale, Sep 01 2023 *)

Extensions

a(39) corrected by Seth A. Troisi, May 18 2022

A327348 The 66 prime dates in each non-leap year of the form concatenate (month,day) without leading zeros for days.

Original entry on oeis.org

11, 13, 17, 19, 113, 127, 131, 23, 29, 211, 223, 227, 31, 37, 311, 313, 317, 331, 41, 43, 47, 419, 421, 53, 59, 521, 523, 61, 67, 613, 617, 619, 71, 73, 79, 719, 727, 83, 89, 811, 821, 823, 827, 829, 97, 911, 919, 929, 101, 103, 107, 109, 1013, 1019, 1021, 1031, 113, 1117, 1123, 1129, 127, 1213, 1217, 1223, 1229, 1231
Offset: 1

Views

Author

Wolfdieter Lang, Sep 30 2019

Keywords

Comments

The months m = 1, 2, ..., 12 contribute 7, 5, 6, 5, 4, 5, 5, 7, 4, 8, 4, 6 such dates respectively. This adds up to 66 prime dates. In leap years there is the additional date 229 (see A327349).

Crossrefs

Cf. A327346 (74 prime dates of the form d.m (no leading 0's for m and d)), A327347 (55 prime dates of the form d.m with leading 0's for m = 1, 3, 7, 9), A327349 (leap year case), A327914 (58 prime dates of the form m.d in non-leap years, with leading 0 for d = 1..9), A327915 (59 prime dates like A327914 but for leap years).

Programs

  • Mathematica
    Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[Join[m, IntegerDigits[#]]] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 28, True, 31]} &, 12], PrimeQ] (* Michael De Vlieger, Oct 03 2019 *)

A327349 The 67 prime dates in each leap year of the form concatenate (month,day) without leading zeros for days.

Original entry on oeis.org

11, 13, 17, 19, 113, 127, 131, 23, 29, 211, 223, 227, 229, 31, 37, 311, 313, 317, 331, 41, 43, 47, 419, 421, 53, 59, 521, 523, 61, 67, 613, 617, 619, 71, 73, 79, 719, 727, 83, 89, 811, 821, 823, 827, 829, 97, 911, 919, 929, 101, 103, 107, 109, 1013, 1019, 1021, 1031, 113, 1117, 1123, 1129, 127, 1213, 1217, 1223, 1229, 1231
Offset: 1

Views

Author

Wolfdieter Lang, Sep 30 2019

Keywords

Comments

In a leap year the months 1, 2, ..., 12 contribute 7, 6, 6, 5, 4, 5, 5, 7, 4, 8, 4, 6 such dates. This adds to 67 prime dates. For non-leap years see the 66 prime dates given in A327348.

Crossrefs

Cf. A327346 (74 prime dates of the form d.m (no leading 0's for m and d)), A327347 (55 prime dates of the form d.m with leading 0's for m = 1, 3, 7, 9), A327348 (non-leap year case), A327914 (58 prime dates of the form m.d in non-leap years, with leading 0 for d = 1..9), A327915 (59 prime dates like A327914 but for leap years).

Programs

  • Mathematica
    Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[Join[m, IntegerDigits[#]]] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 29, True, 31]} &, 12], PrimeQ] (* Michael De Vlieger, Oct 03 2019 *)

A327915 The 59 prime dates of each leap year of the form concatenate(month,day) with leading zero for days 1..9.

Original entry on oeis.org

101, 103, 107, 109, 113, 127, 131, 211, 223, 227, 229, 307, 311, 313, 317, 331, 401, 409, 419, 421, 503, 509, 521, 523, 601, 607, 613, 617, 619, 701, 709, 719, 727, 809, 811, 821, 823, 827, 829, 901, 911, 919, 929, 1009, 1013, 1019, 1021, 1031, 1103, 1109, 1117, 1123, 1129, 1201, 1213, 1217, 1223, 1229, 1231
Offset: 1

Views

Author

Wolfdieter Lang, Sep 30 2019

Keywords

Comments

In leap years all these dates come from the months January, February, ..., December, in the form m.d, with a 0 in front of the days d = 1..9, with 7, 4, 5, 4, 4, 5, 4, 6, 4, 5, 5, 6 prime dates, respectively, adding up to 59. For the corresponding leap year case with 58 prime dates see A327914.
Compared with A327349 (leap years, no 0's before days d = 1..9) one has the same differences as given in a comment in A327914 (229 appears in the present sequence and in A327349).

Crossrefs

Cf. A327346 (74 prime dates d.m without leading 0 for month), A327347 (54 prime dates d.m with leading 0 for months m = 1, 3, 7, 9), A327348 (66 prime dates m.d for non-leap years), A327349 (67 prime dates, like A327348 but for leap years), A327914 (58 prime dates, the case for non-leap years).

Programs

  • Mathematica
    Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[m~Join~PadLeft[IntegerDigits[#], 2]] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 29, True, 31]} &, 12], PrimeQ] (* Michael De Vlieger, Oct 03 2019 *)
fd[{m_,d_}]:=FromDigits[Flatten[{m,PadLeft[{d},2,0]}]]; Select[fd[Take[#,{2,3}]]&/@ DateRange[ {2024,1,1},{2024,12,31}],PrimeQ] (* Harvey P. Dale, Sep 01 2023 *)

A327347 The 54 prime dates of each year of the form concatenate(day,month) with leading zero for months 1, 3, 7, 9 (no leading zero for days).

Original entry on oeis.org

101, 401, 601, 701, 1201, 1301, 1601, 1801, 1901, 2801, 3001, 103, 503, 1103, 1303, 2003, 2203, 2503, 2803, 2903, 107, 307, 607, 907, 1307, 1607, 1907, 2207, 2707, 109, 409, 509, 709, 809, 1009, 1109, 1409, 1609, 1709, 2309, 2609, 2909, 211, 311, 811, 911, 1511, 1811, 2011, 2111, 2311, 2411, 2711, 3011
Offset: 1

Views

Author

Wolfdieter Lang, Sep 30 2019

Keywords

Comments

All these dates come from January, March, July, September and November, sorted this d.m way, with 11, 9, 9, 13 and 12 dates, respectively, summing to 54. Note that all September dates without leading zero of month m = 9 from A327346 survive after inserting the 0. The November dates coincide, of course.

Crossrefs

Cf. A062800 (first 11 members), A101780 (9 members, starting with n = 2), A166547 (9 members, starting with n = 2), A166560 (first 13 members), A167442 (12 members, starting with n = 2), respectively.
Cf. A327346 (74 prime dates d.m without leading 0 for month), A327348 (66 prime dates m.d for non-leap years), A327349 (67 prime dates, like A327348 but for leap years), A327914 (58 prime dates m.d for non-leap years, with leading 0 for d = 1..9), A327915 (59 prime dates, like A327914, but for leap years).

Programs

  • Mathematica
    Select[Flatten@ Map[Function[{m, d},  Array[FromDigits[IntegerDigits[#]~Join~m] &, d]] @@ {PadLeft[IntegerDigits@ #, 2], Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 28, True, 31]} &, Select[Range[1, 12, 2], CoprimeQ[#, 10] &]], PrimeQ] (* Michael De Vlieger, Oct 03 2019 *)

A327920 The 16 pure prime dates of each year of the form concatenate(day,month) with month and day also prime numbers.

Original entry on oeis.org

23, 53, 73, 113, 173, 193, 233, 293, 313, 37, 137, 197, 317, 211, 311, 2311
Offset: 1

Views

Author

Wolfdieter Lang, Oct 08 2019

Keywords

Comments

For the case of the 16, respectively 17, pure prime dates of the form concatenate(month,day) see A327918 (non-leap years) and A327919 (leap years).
Only the three months m = 3, 7, and 11 qualify. The qualifying days are for November (m = 11): d = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and for months March and July (m = 3 and 7): d = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.
The months m = 3, 7, 11 contribute 9, 4, 3 dates, respectively, adding to 16.

Crossrefs

Cf. A055782 (first nine terms), A055783 (first four terms), A114007 (three terms starting with n = 8). A327346 (with d and m also nonprime allowed), A327918, A327919.

Programs

  • Mathematica
    Select[Flatten[Table[d*10^IntegerLength[m]+m,{m,{3,7,11}},{d,Prime[ Range[ 11]]}]],PrimeQ] (* Harvey P. Dale, May 24 2022 *)
Showing 1-6 of 6 results.

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