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 1-5 of 5 results.

A071612 a(n) is the smallest prime that is the first of n consecutive primes which are all emirps.

Original entry on oeis.org

13, 13, 71, 733, 1193, 1193, 1193, 1193, 1193, 1193, 1477271183, 9387802769, 15423094826093
Offset: 1

Views

Author

Klaus Brockhaus, May 27 2002

Keywords

Examples

			1193,1201,1213,1217,1223,1229,1231,1237,1249,1259 are ten consecutive primes which are all emirps and 1193,1201,1213,1217,1223 is the first occurrence of five consecutive primes which are all emirps, so a(5) = a(6) = a(7) = a(8) = a(9) = a(10) = 1193.

Links

Crossrefs

Cf. A006567, A070905, A071614, A103172.

Extensions

By studying terms of the sequence A103172 we can deduce that a(11), a(12) are 1477271183 & 9387802769. - Farideh Firoozbakht, Jun 17 2010
a(13) from Giovanni Resta, Apr 23 2021

A071613 a(n) is the smallest prime that is the first of n consecutive primes with equal digit sum.

Original entry on oeis.org

2, 523, 22193, 1442173, 5521819, 354963229, 881160173, 881160173, 441586802467, 3085029222449
Offset: 1

Views

Author

Klaus Brockhaus, May 27 2002

Keywords

Comments

a(11) > 10^14. - Giovanni Resta, Aug 15 2013

Examples

			a(3) = 22193, since 22193,22229,22247 are three consecutive primes with digit sum 17 and this is the first occurrence of three consecutive primes with equal digit sum.

Crossrefs

Cf. A006567, A070905, A071614.

Extensions

a(7)-a(9) from Donovan Johnson, Dec 02 2009
a(10) from Giovanni Resta, Aug 14 2013

A071614 a(n) is the smallest emirp that is the first of n consecutive emirps with equal digit sum.

Original entry on oeis.org

13, 79, 15919, 197837, 3528871, 110539181, 731854429, 9819391129
Offset: 1

Views

Author

Klaus Brockhaus, May 27 2002

Keywords

Comments

a(9) > 10^11. - Donovan Johnson, Nov 07 2010

Examples

			a(3) = 15919, since 15919,15937,15973 are three consecutive emirps with digit sum 25 and this is the first occurrence of three consecutive emirps with equal digit sum.

Crossrefs

Cf. A006567, A070905, A071612, A071613.

Extensions

a(7)-a(8) from Donovan Johnson, Nov 07 2010

A171490 Numbers for which the smallest number of steps to reach 1 in "3x+1" (or Collatz) problem is a prime.

Original entry on oeis.org

1, 5, 7, 12, 14, 16, 29, 51, 56, 58, 60, 64, 65, 67, 74, 75, 78, 83, 87, 90, 100, 102, 104, 106, 109, 115, 118, 119, 122, 128, 130, 132, 134, 141, 142, 147, 161, 166, 173, 176, 187, 188, 200, 212, 219, 221, 231, 234, 239, 241, 251, 259, 264, 293, 313, 314, 316
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 10 2009

Keywords

Comments

Positions of primes in A033491. [R. J. Mathar, Nov 01 2010]

Examples

			1st Collatz sequence with a(1)=1 step starts with 2=prime(1): 2-1;
1st Collatz sequence with a(3)=7 steps starts with 3=prime(2): 3-10-5-16-8-4-2-1;
prime(6)=13 has Collatz sequence with 9 steps: 13-40-20-10-5-16-8-4-2-1, so has the smaller composite 12 < 13: 12-6-3-10-5-16-8-4-2-1 => 9 not a term of sequence;
1st Collatz sequence with a(5)=14 steps starts with 11=prime(5): 11-34-17-52-26-13-40-20-10-5-16-8-4-2-1.

References

  • R. K. Guy, "Collatz's Sequence" in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 215-218, 1994
  • Clifford A. Pickover, Wonders of Numbers, Oxford University Press, pp. 116-118, 2001

Links

Crossrefs

Cf. A070905, A033491, A088975, A126727, A060565

Extensions

Terms > 187 from R. J. Mathar, Nov 01 2010
Name edited by Michel Marcus, Jul 07 2018

A171619 Primes in A171490.

Original entry on oeis.org

5, 7, 29, 67, 83, 109, 173, 239, 241, 251, 293, 313, 337, 367, 571, 613, 769, 821, 877, 941, 947, 1031, 1069, 1103, 1511, 1693, 1759, 1901, 2011
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 13 2009

Keywords

Comments

Terms of sequence are primes in growing order where smallest number of steps m to reach 1 in "3x+1" (or Collatz) problem is a prime too.

Examples

			(1) 1st Collatz sequence with 5=prime(3) steps starts with 5=prime(3): 5-16-8-4-2-1, gives a(1)=5.
(2) 1st Collatz sequence with 7=prime(4) steps starts with 3=prime(2): 3-10-5-16-8-4-2-1, gives a(2)=7.
(3) 1st Collatz sequence with 29=prime(10) steps starts with 43=prime(14): 43-130-65-196-98-49-148-74-37-112-56-28-14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1, gives a(3)=29.
(4) List of prime steps m for above a(n): 5, 3, 43, 167, 233, 41, 937, 14831, 9887, 7963, 73063, 45127, 78791, 225023, 6956969, 10998599, 126357223, 859130059, 2845683047, 322623647, 95592191, 8363817307, 28677246203, 38590505339, 35521451596571, 478672174364191, 1168778549494463, 6376392739978081, 103147916159472367.

References

  • R. K. Guy, "Collatz's Sequence" in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 215-218, 1994.
  • Clifford A. Pickover, Wonders of Numbers, Oxford University Press, pp. 116-118, 2001.
  • Guenther J. Wirsching, The Dynamical System Generated by the 3n+1 Function, Springer-Verlag, Berlin, 1998.

Links

Crossrefs

Cf. A070905, A033491, A088975, A126727, A060565, A171490.

Extensions

Missing term a(7)=173 inserted by Georg Fischer, Oct 26 2022
a(23)-a(29) (using Eric Roosendaal's data) by Tyler Busby, Feb 11 2023
Showing 1-5 of 5 results.

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