A050236 -id:A050236 - cp's OEIS frontend

A050239 Consecutive square palindromic primes; palindromic primes of the form x^2 + (x+1)^2, where x values are given by A050236.

Original entry on oeis.org

5, 181, 313, 3187813

Offset: 1

Eric W. Weisstein

No other terms < 10^20. - Patrick De Geest, Aug 15 1999

Patrick De Geest, Palindromic Sums of Squares of Consecutive Integers
Carlos Rivera, Puzzle 14. Pal-Primes and sum of powers, The Prime Puzzles & Problems Connection.
Eric Weisstein's World of Mathematics, Palindromic Prime

Cf. A050236.

Subsequence of A002385.

Select[Total/@Partition[Range[1300]^2,2,1],PalindromeQ[#]&&PrimeQ[#]&] (* Harvey P. Dale, Aug 19 2022 *)

A027571 Numbers k such that k^2 + (k+1)^2 is palindromic.

Original entry on oeis.org

0, 1, 9, 12, 16, 919, 1257, 1262, 1621, 1706, 170706, 904280, 1258182, 7901014, 8659929, 12458597, 17070706, 80472264, 1616689803, 1680689788, 1705387643, 7360311900, 8032814139, 8055329360, 12574461617, 16794058711, 165058650666, 844706005220, 1250999800012, 1255589965852

Offset: 1

Patrick De Geest

a(50) > 70710678118654752440. - Patrick De Geest, May 25 2021

Patrick De Geest, Table of n, a(n) for n = 1..49 (terms a(1)..a(29) from Giovanni Resta)
Patrick De Geest, Palindromic Sums of Squares of Consecutive Integers
Patrick De Geest, Palindromic Centered Polygonal Numbers

Cf. A001844, A027572, A050236, A050239.

A050236 is a subsequence.

isok(m) = my(d=digits(m^2+(m+1)^2)); d == Vecrev(d); \\ Michel Marcus, Jan 05 2019

a(18)-a(21) from Donovan Johnson, Aug 26 2012
a(22)-a(29) from Giovanni Resta, Aug 06 2019
a(1)=0 added by Patrick De Geest, May 25 2021

A027572 Palindromes of form n^2 + (n+1)^2.

Original entry on oeis.org

1, 5, 181, 313, 545, 1690961, 3162613, 3187813, 5258525, 5824285, 58281418285, 1635446445361, 3166046406613, 124852060258421, 149988757889941, 310433303334013, 582818040818285, 12951570707515921, 5227371841481737225, 5649436330336349465, 5816694029204966185

Offset: 1

Patrick De Geest

a(50) > 10^40. - Patrick De Geest, May 25 2021

Patrick De Geest, Table of n, a(n) for n = 1..49
Patrick De Geest, Palindromic Sums of Squares of Consecutive Integers
Patrick De Geest, Palindromic Centered Polygonal Numbers

Cf. A001844, A027571, A050236, A050239.

A050239 is a subsequence.

Select[Total/@Partition[Range[0,2000]^2,2,1],PalindromeQ] (* The program generates the  first 10 terms of the sequence. *) (* Harvey P. Dale, Jan 19 2025 *)

a(n) = (4*m^2 - 4*m + 2)/2 = (m-1)^2 + m^2 or a(n) = (4*n^2 + 4*n + 2)/2 = n^2 + (n+1)^2 with n = m - 1.

a(18)-a(21) from Donovan Johnson, Aug 26 2012
a(1)=1 added by Philip Mizzi, Sep 02 2019
a(22)-a(49) from Patrick De Geest, May 25 2021

cp's OEIS Frontend

A050239 Consecutive square palindromic primes; palindromic primes of the form x^2 + (x+1)^2, where x values are given by A050236.

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A027571 Numbers k such that k^2 + (k+1)^2 is palindromic.

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A027572 Palindromes of form n^2 + (n+1)^2.

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