A115739 -id:A115739 - cp's OEIS frontend

A115738 k is prime and digits of k^2 include digits of k as substring.

5, 66952741, 146509717, 753348181, 562984507451, 860628177919, 978058181203, 50385563791193

Offset: 1

Giovanni Resta, Jan 30 2006

Subset of A046831.

a(9) > 10^14. Primes 43473168442554675203, 20944025626422831137347, 35083931242599287584057, and 569177878099445999493598065089 are also terms. - Giovanni Resta, Sep 10 2018

			66952741^2 = 4482_66952741_3081.

Cf. A046831, A115739, A115763.

a(8) from Giovanni Resta, Sep 08 2018

A115762 Numbers k such that the digits of k^3, reversed, include the digits of k as substring.

Original entry on oeis.org

1, 4, 5, 6, 9, 39, 67, 99, 670, 735, 999, 2424, 5619, 6700, 6966, 9999, 14597, 15458, 29266, 33795, 43259, 49664, 61256, 69566, 75463, 80238, 97155, 99999, 123798, 190544, 290105, 292660, 424068, 424846, 429163, 432590, 625503, 658458

Offset: 1

Giovanni Resta, Jan 30 2006

			735^3 = 39706(537)5.

Cf. A115761, A115763, A115764, A115739.

Select[Range[660000],SequenceCount[IntegerDigits[IntegerReverse[#^3]],IntegerDigits[#]]>0&] (* Harvey P. Dale, May 13 2025 *)

A115764 Primes p such that the digits of p^3, reversed, include the digits of p as a substring.

Original entry on oeis.org

5, 67, 695263, 994871, 5616469, 31471711, 43693817, 878757569, 5149409929, 7866434053, 8603497223, 13880125751

Offset: 1

Giovanni Resta, Jan 30 2006

			31471711^3 = 3(11717413)21891966598431.

Cf. A115761, A115762, A115763, A115739.

A273007 a(n) is the smallest exponent > 1 such that p^a(n) ends with p, where p is the n-th prime.

Original entry on oeis.org

5, 5, 2, 5, 11, 21, 21, 11, 21, 11, 11, 21, 6, 5, 21, 21, 11, 6, 21, 11, 21, 11, 21, 11, 21, 11, 101, 21, 51, 101, 101, 51, 101, 51, 11, 11, 21, 101, 101, 101, 51, 51, 51, 5, 101, 11, 51, 101, 101, 51, 101, 51, 26, 3, 21, 101, 51, 51, 101, 26, 101, 21, 5, 51

Offset: 1

Paolo P. Lava, May 24 2016

			2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32;
3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243.

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Cf. A051248, A115739, A273527.

P:=proc(q) local d,k,n; for n from 1 to q do if isprime(n) then d:=ilog10(n)+1;
for k from 2 to q do if n=(n^k mod 10^d) then print(k); break; fi; od; fi; od; end: P(10^3);

Table[Length[NestWhileList[p #&,p^2,Mod[#,10^IntegerLength[p]]!=p&]]+1,{p,Prime[ Range[65]]}] (* Harvey P. Dale, Jul 25 2019 *)

cp's OEIS Frontend

A115738 k is prime and digits of k^2 include digits of k as substring.

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A115762 Numbers k such that the digits of k^3, reversed, include the digits of k as substring.

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A115764 Primes p such that the digits of p^3, reversed, include the digits of p as a substring.

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Examples

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A273007 a(n) is the smallest exponent > 1 such that p^a(n) ends with p, where p is the n-th prime.

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