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.

A226092 Fourth powers that become prime when their most significant (leftmost) decimal digit is removed.

Original entry on oeis.org

2401, 279841, 15752961, 20151121, 35153041, 43046721, 62742241, 68574961, 88529281, 200533921, 260144641, 547981281, 671898241, 2385443281, 2655237841, 2750058481, 2847396321, 3262808641, 3722098081, 4640470641, 5887339441, 6414247921, 8428892481, 8882874001
Offset: 1

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Author

Jonathan Vos Post, May 26 2013

Keywords

Comments

This is to fourth powers A000583 as A226090 is to as cubes A000578, and as A225873 is to squares A000290.

Examples

			a(1) = 7^4 = 2401, because removing the leftmost digit (4) leaves 401, which is prime.
a(2) = 23^4 = 279841, because removing the leftmost digit (2) leaves 79841, which is prime.
a(3) = 63^4 = 15752961, because removing the leftmost digit (1) leaves 5752961, which is prime.
a(10) = 119^4 = 200533921, because removing the leftmost digit (2) leaves 00533921 = 533921, which is prime.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[307]^4, PrimeQ@Mod[#, 10^IntegerLength@#/10] &] (* Giovanni Resta, May 26 2013 *)

Extensions

a(13)-a(24) from Giovanni Resta, May 26 2013

A226531 Cubes that become prime when their least-significant (rightmost) digit is removed.

Original entry on oeis.org

27, 3375, 4096, 4913, 35937, 97336, 110592, 148877, 421875, 681472, 1191016, 1442897, 1560896, 2628072, 3241792, 3581577, 3869893, 4741632, 5359375, 8998912, 10218313, 12649337, 16777216, 16974593, 21253933, 26730899, 31255875, 32157432, 43986977, 45882712
Offset: 1

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Author

Keywords

Examples

			4096 = 16^3, and becomes the prime number 409 when truncated.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[1000]^3,PrimeQ[Floor[#/10]]&] (* Harvey P. Dale, May 28 2021 *)
  • R
    library(gmp)trimR=function(x) { x=as.character(x); ifelse(nchar(x)<2,0,substr(x,1,nchar(x)-1)) }
    y=as.bigz(rep(0,10000)); len=0; n=as.bigz(-1)
    while(len<10000) if(isprime(trimR((n=n+1)^3))) y[(len=len+1)]=n^3

A226098 Fifth powers that become prime when their most significant (leftmost) decimal digit is removed.

Original entry on oeis.org

32, 243, 59049, 161051, 371293, 6436343, 14348907, 115856201, 282475249, 844596301, 73439775749, 173726604657, 312079600999, 779811265199, 2553954421743, 2817036000549, 3515706497843, 5798839393557, 10112638401999, 12914277518099, 14530697473149
Offset: 1

Views

Author

Jonathan Vos Post, May 26 2013

Keywords

Comments

This is to fifth powers A000584 as A226092 is to fourth powers A000583, as A226090 is to as cubes A000578, and as A225873 is to squares A000290.

Examples

			a(1) = 2^5 = 32 because when its most significant (or leftmost) digit (3) is removing the remaining 2 is prime.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[500]^5,PrimeQ[FromDigits[Rest[IntegerDigits[#]]]]&] (* Harvey P. Dale, Nov 10 2021 *)

A226100 Main diagonal A(n,n) of matrix A(k,n) = n-th k-th power that becomes prime when its most significant (i.e., leftmost) decimal digit is removed.

Original entry on oeis.org

12, 289, 729, 20151121, 371293, 2839760855281, 24160660561265139, 241100240228887100161, 3421941488772218992567, 845219547726738091164049, 7506514445791062595879589895041, 293936151563356954592299567713259041, 6657844787831219696900816415217242830357
Offset: 1

Views

Author

Jonathan Vos Post, May 26 2013

Keywords

Comments

Row 1 = A(1,n) = A226099. Row 2 = A(2,n) = A225873. Row 3 = A(3,n) = A226090. Row 4 = A(4,n) = A226092. Row 5 = A(5,n) = A226098.

Examples

			a(1) = A(1,1) = 12 = first number whose first power (itself) becomes prime when its most significant (or leftmost) digit is removed.
a(2) = A(2,2) = 289 = second square which becomes prime when its most significant (or leftmost) digit is removed.
a(3) =
		

Crossrefs

Showing 1-4 of 4 results.