A050239 -id:A050239 - cp's OEIS frontend

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

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

A050236 Indices of consecutive squares palindromic primes; x such that x^2 + (x+1)^2 is palindromic and prime.

Original entry on oeis.org

1, 9, 12, 1262

Offset: 1

Eric W. Weisstein

No other terms < 20000000000. - 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. A050239.

Intersection of A027861 and A027571.

Flatten[Position[Total/@Partition[Range[1300]^2,2,1],?(PrimeQ[#] && IntegerDigits[#]==Reverse[IntegerDigits[#]]&)]] (* _Harvey P. Dale, Dec 09 2014 *)

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

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

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

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A050236 Indices of consecutive squares palindromic primes; x such that x^2 + (x+1)^2 is palindromic and prime.

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

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