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.

A101116 Values in A101115 which are records.

Original entry on oeis.org

0, 5, 9, 14, 15, 18, 19, 20, 22
Offset: 1

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Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004

Keywords

Comments

All primes up to 1000003 have been tested.

Crossrefs

Programs

  • Python
    from sympy import isprime, nextprime
    def agen(): # generator of tuple of terms of (A101116, A101117, A101118)
        n, pn, record = 0, 1, -1
        while True:
            n += 1
            pn = nextprime(pn)
            s, c, found = str(pn), 0, True
            while found:
                found = False
                for d in "123456789":
                    if isprime(int(d+s)):
                        s, c, found = d+s, c+1, True
                        break
            if c > record:
                record = c
                yield record, pn, int(s)
    g = agen()
    print([next(g)[0] for n in range(1, 7)]) # Michael S. Branicky, Jun 24 2022

Extensions

a(7)-a(8) from Michael S. Branicky, Jun 24 2022
a(9) from Michael S. Branicky, Jul 26 2024

A101118 a(n) = the resulting prime generated when the process described in A101115 is applied to A101117(n).

Original entry on oeis.org

2, 612113, 5372126317, 4818372912366173, 21291981879276213799, 912733515196363393600307, 668334992181698187977197951, 231879245133561335194866134641, 933651219687395363156136052921903
Offset: 1

Views

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004

Keywords

Examples

			a(3) = 5372126317 because 5372126317 is the last prime that can be generated by successively prepending nonzero digits to A101117(3). A101117(3) is 7. A101116(3) indicates that 9 digits can be successively prepended to 7 generating a new prime each time. Doing so and giving preference to the smallest digit which meets the requirement, generates the following primes: 17, 317, 6317, 26317, 126317, 2126317, 72126317, 372126317, 5372126317.
		

Crossrefs

Programs

  • Python
    g = agen() # uses agen() and imports from A101116
    print([next(g)[2] for n in range(1, 7)]) # Michael S. Branicky, Jun 24 2022

Extensions

a(7)-a(8) and typo corrected in a(6) from Michael S. Branicky, Jun 24 2022
a(9) from Michael S. Branicky, Jul 26 2024

A101117 a(n) = the first prime yielding the record value A101116(n).

Original entry on oeis.org

2, 3, 7, 73, 13799, 600307, 77197951, 4866134641, 36052921903
Offset: 1

Views

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004

Keywords

Examples

			a(6) = 600307 because 600307 is the first prime to which A101116(6) digits (18) can be prepended yielding a new prime each time (giving preference to the smallest digit which meets the requirement) - 600307, 3600307, 93600307, ..., 9912733515196363393600307.
		

Crossrefs

Programs

  • Python
    g = agen() # uses agen() and imports from A101116
    print([next(g)[1] for n in range(1, 7)]) # Michael S. Branicky, Jun 24 2022

Extensions

a(7)-a(8) from Michael S. Branicky, Jun 24 2022
a(9) from Michael S. Branicky, Jul 26 2024

A259848 Suffixes of 4818372912366173 (all primes).

Original entry on oeis.org

3, 73, 173, 6173, 66173, 366173, 2366173, 12366173, 912366173, 2912366173, 72912366173, 372912366173, 8372912366173, 18372912366173, 818372912366173, 4818372912366173
Offset: 1

Views

Author

Keywords

Examples

			.......................3
.......................73
.......................173
.......................6173
.......................66173
.......................366173
.......................2366173
.......................12366173
.......................912366173
.......................2912366173
.......................72912366173
.......................372912366173
.......................8372912366173
.......................18372912366173
.......................818372912366173
.......................4818372912366173
		

Crossrefs

Formula

a(n) = 4818372912366173 mod 10^n.
Showing 1-4 of 4 results.