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 1-3 of 3 results.

A343714 Palindromic primes of the form p//q//reverse(p), where p is a prime (not necessarily palindromic) and q, of course, is a palindromic prime.

Original entry on oeis.org

353, 373, 727, 757, 11311, 13331, 19391, 31013, 31513, 33533, 37273, 37573, 39293, 71317, 71917, 73237, 77977, 79397, 97379, 97579, 1035301, 1092901, 1093901, 1175711, 1178711, 1273721, 1317131, 1335331, 1338331, 1513151, 1572751, 1633361, 1737371, 1793971
Offset: 1

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Author

Jon E. Schoenfield, May 08 2021

Keywords

Comments

Note that reverse(p) need not be a prime; e.g., a(7)=19391 is the concatenation of 19, 3, and 91=7*13. If a requirement were added that reverse(p) also be a prime, the result would be sequence A343715.

Examples

			353 is a term because it is a palindromic prime (A002385) and is the concatenation of 3 (a prime), 5 (a palindromic prime), and 3 (the reverse of 3).
31513 is a term in two ways: as the concatenation 3//151//3 and as the concatenation 31//5//13.
7392937 is a term in three ways: 7//39293//7, 73//929//37, and 739//2//937.
		

Crossrefs

A343715 Palindromic primes of the form p//q//reverse(p), where p, q, and reverse(p) are primes.

Original entry on oeis.org

353, 373, 727, 757, 11311, 13331, 31013, 31513, 33533, 37273, 37573, 39293, 71317, 71917, 73237, 77977, 79397, 97379, 97579, 1175711, 1178711, 1317131, 1335331, 1338331, 1513151, 1572751, 1737371, 1793971, 1917191, 1993991, 1995991, 3103013, 3106013, 3127213
Offset: 1

Views

Author

Jon E. Schoenfield, May 08 2021

Keywords

Comments

If reverse(p) were allowed to be nonprime, the result would be sequence A343714, which includes such terms as 19391.

Examples

			353 is a term because it is a palindromic prime (A002385) and is the concatenation of 3 (a prime), 5 (a palindromic prime), and 3 (the reverse of 3, and also a prime).
31513 is a term in two ways: as the concatenation 3//151//3 and as the concatenation 31//5//13.
7392937 is a term in three ways: 7//39293//7, 73//929//37, and 739//2//937.
		

Crossrefs

A178496 The smallest palindromic prime which contains the decimal expansion of 11^n in its decimal representation.

Original entry on oeis.org

11, 11, 1212121, 133111331, 361464163, 31501610513, 916517717715619, 1017178491948717101, 111888534121435888111, 1967497532357947691, 11064247395259374246011, 142853116706111607611358241
Offset: 0

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 28 2010

Keywords

Comments

The entries have two possible formats: a//11^n ( = 11^n//b), where the double-slash denotes concatenation, or c//11^n//d.
By definition, the concatenation has to be a palindromic prime, A002385.

Examples

			a(0) = 11^0//1 = 1//1 = palprime(5).
a(1) = 11^1 = 11.
a(2) = 1212//11^2 = 1212//121 = palprime(151).
a(3) = 13311//11^3 = 13311//1331 = palprime(1270).
a(4) = 36//11^4//63 = 36//14641//63 = palprime(3035).
a(5) = 3150//11^5//3 = 3150//161051//3 = palprime(18465).
a(6) = 9165177//11^6//9 = 9165177//1771561//9.
a(7) = 101717849//11^7//01 = 101717849//19487171//01.
a(8) = 1118885341//11^8//11 = 1118885341//214358881//11.
a(9) = 196749753//11^9 = 196749753//2357947691.
a(10) = 11064247395//11^10//1 = 11064247395//25937424601//1.
a(11) = 14//11^11//1607611358241 = 14//285311670611//1607611358241.
a(12) = 111276738248//11^12//11 = 111276738248//3138428376721//11.
		

Crossrefs

Showing 1-3 of 3 results.